You measure the power delivered by a battery to be 1.15 W when it is connected in series with two equal resistors. How much power will the same battery deliver if the resistors are now connected in parallel across it

Explanation:

The relationship between electric force and distance between charged objects is given by the formula as follows :

[tex]F=\dfrac{kq_1q_2}{d^2}[/tex]

k is electrostatic constant and d is distance between charges

The electric force between charges is inversely proportional to the square of distance between them.

Answer:

The location are [tex]x_1 = 2 \ and \ x_2 = 3[/tex]

Explanation:

From the question we are told that

    The potential energy is  [tex]U(x) = (2.0 \ J/m^3) * x^3 - (15 \ J/m) * x^2 + (36 \ J/m) * x - 23 \ J[/tex]

The force on the mass can be mathematically evaluated as  

      [tex]F = - \frac{d U(x)}{d x } = -( 6 x^2 - 30x +36)[/tex]

The negative sign shows that the force is moving in the opposite  direction of the potential energy

       [tex]F = - 6 x^2 + 30x - 36[/tex]

At critical point

      [tex]\frac{d U(x)}{dx} = 0[/tex]

So  

     [tex]- 6 x^2 + 30x - 36 = 0[/tex]

     [tex]- x^2 + 5x - 6 = 0[/tex]

Using quadratic equation formula to solve this we have that

       [tex]x_1 = 2 \ and \ x_2 = 3[/tex]

Answer:

λ1 = 0.0129m = 1.29cm

λ2 = 0.00923m = 0.92 cm

Explanation:

To find the distance between the first order bright fringe and the central peak, can be calculated by using the following formula:

[tex]y_m=\frac{m\lambda D}{d}[/tex]    (1)

m: order of the bright fringe = 1

λ: wavelength of the light = 660 nm, 470 nm

D: distance from the screen = 5.50 m

d: distance between slits = 0.280mm = 0.280 *10^⁻3 m

ym: height of the m-th fringe

You replace the values of the variables in the equation (1) for each wavelength:

For λ = 660 nm = 660*10^-9 m

[tex]y_1=\frac{(1)(660*10^{-9}m)(5.50m)}{0.280*10^{-3}m}=0.0129m=1.29cm[/tex]

For λ = 470 nm = 470*10^-9 m

[tex]y_1=\frac{(1)(470*10^{-9}m)(5.50m)}{0.280*10^{-3}m}=0.00923m=0.92cm[/tex]

Answer: in this question, the only charge in the cavity is Q. Inside the conducting spherical shell, the electric field is zero.

While outside the shell, the electric field is given by: k(q + Q)/r²

Where;

K= is a constant which is given as, 8.99 x 10^9 N m² / C².

Q= source charge which creates the electric field

q= is the test charge which is used to measure the strength of the electric field at a given location.

r= is the radius

Explanation: Inside the conducting spherical shell, the electric field is zero since the Electric field vanishes everywhere inside the volume of a good conductor.

Answer:

a.  4 V

b. 0.697 A

Explanation:

Magnetic field strength B =  0.732 T

length of rod l = 0.362 m

velocity of rod v = 15.1 m/s

a.  EMF can be calculated as

E = Blv = 0.732 x 0.362 x 15.1 = 4 V

b. If the rod is connected to a conducting rail, with resistance R = 5.74Ω

current I = V/R = 4/5.74 = 0.697 A

the current flows in a clockwise direction

Answer:

v = 1.4 m/s

Explanation:

This problem is about an inelastic collision. The total momentum before the collision is equal to total momentum after (because of the conservation of momentum law):

[tex]m_1v_1-m_2v_2=(m_1+m_2)v[/tex]  (1)

m1: mass of the toy car = 2 kg

m2: mass of the toy truck = 3 kg

v1: speed of the toy car = 1 m/s

v2: speed of the truck car = 3 m/s

v: speed of both car and truck after the collision = ?

In the equation (1) the negative sign of m2v2 is because of the opposite direction of the toy truck respect to the toy car.

You solve the equation (1) for v, and you replace the values of all variables involved:

[tex]v=\frac{m_1v_1-m_2v_2}{m_1+m_2}\\\\v=\frac{(2kg)(1m/s)-(3kg)(3m/s)}{2kg+3kg}=-1.4\frac{m}{s}[/tex]

this velocity is negative, then, the direction of motion of both car and truck is in the direction of the truck

Hence, the speed of both car and truck toys is 1.4 m/s

Answer:

(a) v-bullet = 399.04 m/s

(b) I = 2.38 kg m/s

(c) T = 2.59 N

Explanation:

(a) To calculate the initial speed of the bullet, you first take into account that the kinetic energy of both wood block and bullet, just after the bullet impacts the block, is equal to the potential gravitational energy of block and bullet when the cord is at 60° respect to the vertical.

The potential energy is given by:

[tex]U=(M+m)gh[/tex]       (1)

U: potential energy

M: mass of the wood block = 1 kg

m: mass of the bullet = 6g = 6.0*10^-3 kg

g: gravitational constant = 9.8m/s^2

h: distance to the ground

The distance to the ground is calculate d by using the information about the length of the cord and the degrees of the cord respect to the vertical:

[tex]h=l-lsin\theta\\\\h=2.2m-2,2m\ sin60\°=0.29m[/tex]

The potential energy is:

[tex]U=(1kg+6*10^{-3}kg)(9.8m/s^2)(0.29m)=2.85J[/tex]

Next, the potential energy is equal to kinetic energy of the block and the bullet at the beginning of its motion:

[tex]U=\frac{1}{2}(M+m)v^2\\\\v=\sqrt{2\frac{U}{M+m}}=\sqrt{2\frac{2.85J}{1kg+6*10^{-3}kg}}=2.38\frac{m}{s}[/tex]

Next, you use the momentum conservation law, in order to calculate the speed of the bullet before the impact:

[tex]Mv_1+mv_2=(M+m)v[/tex]    (2)

v1: initial velocity of the wood block = 0m/s

v2: initial speed of the bullet

v: speed of bullet and block = 2.38m/s

You solve the equation (2) for v2:

[tex]M(0)+mv_2=(M+m)v[/tex]    

[tex]v_2=\frac{M+m}{m}v=\frac{1kg+6*10^{-3}kg}{6*10^{-3}kg}(2.38m/s)\\\\v_2=399.04\frac{m}{s}[/tex]

The speed of the bullet before the impact with the wood block is 399.04 m/s

(b) The impulse is gibe by the change in the velocity of the block, multiplied by the mass of the block:

[tex]I=M\Delta v=M(v-v_1)=(1kg)(2.38m/s-0m/s)=2.38kg\frac{m}{s}[/tex]

The impulse is 2.38 kgm/s

(c) The force on the cord after the impact is equal to the centripetal force over the block and bullet. That is:

[tex]T=F_c=(M+m)\frac{v^2}{l}=(1.006kg)\frac{(2.38m/s)^2}{2.2m}=2.59N[/tex]    

The force on the cord after the impact is 2.59N

Answer:

Explanation:

Apply the law of conversion of energy

[tex]V_f = \sqrt{2gh}[/tex]

where,

h = height of which the bullet and block rise after impact

[tex]h = L - Lcos\theta\\\\h = 2.2 - (2.2*cos60)\\\\h = 1.1m[/tex]

Therefore,

[tex]V_f = \sqrt{2gh}\\\\V_f = \sqrt{2*9.8*1.1}\\\\V_f = 4.64m/s[/tex]

From conservation of momentum principle, [tex]m_Bv_B = 0[/tex]

[tex]m_ov_o + m_Bv_B = (m_b+m_B)V_f\\\\0.006V_o = (0.006+1)*4.64\\\\V_o = 777.97m/s[/tex]

C) The force in the cable is due to the centrfugal force of the system, which is due to the motion of the system is a curved path and weight of the system

[tex]F = \frac{m_b+m_B}{L}V_f^2 + (m_b+m_B)g\\\\F = \frac{0.006+1}{2.2}*4.64^2 + (0.006+1)9.81\\\\F = 19.71N[/tex]

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Answer:

N₂ / N₁ = 13.3

Explanation:

A transformer is a system that induces a voltage in the secondary due to the variation of voltage in the primary, the ratio of voltages is determined by the expression

           ΔV₂ = N₂ /N₁  ΔV₁

where ΔV₂ and ΔV₁ are the voltage in the secondary and primary respectively and N is the number of windings on each side.

In this case, they indicate that the primary voltage is 9.0 V and the secondary voltage is 120 V

therefore we calculate the winding ratio

         ΔV₂ /ΔV₁ = N₂ / N₁

         N₂ / N₁ = 120/9

         N₂ / N₁ = 13.3

s good clarify that in transformers the voltage must be alternating (AC)

Answer:

Loudness: decreases

Amplitude: decreases

Pitch: stays the same

Frequency: stays the same

Explanation:

1.

An oscilloscope measures how much the microphone is vibrating, or how much electricity it is sending. This means that a louder noise will register higher on the oscilloscope. Since the size of the waves at Y is lower than at X, the loudness of the sound has decreased.

2.

Similarly to loudness, amplitude measures how far the crests of the waves are from the nodes. Since Y is closer to the center line than X, it has a lower amplitude.

3 and 4.

The pitch and frequency, for our purposes, are essentially the same thing here. They are dependent on how close together the waves on the oscilloscope are, or how quickly the microphone is vibrated. Since this stays the same throughout the entire sound, they both stay the same.

Hope this helps!

Answer:

either +z direction or -z direction.

Explanation:

The direction of the electric field, in an electromagnetic wave always is perpendicular to the direction of the magnetic field and the direction of propagation of the wave.

You assume a system of coordinates with the negative x axis as the west direction, and the y axis as the up direction

In this case, the wave is propagating toward the west (- x direction), and the magnetic field vector points up (+ y direction), then, it is mandatory that the electric field vector points either +z direction or -z direction.

Answer:

a) v = -30 - 32 t ,  s (t) = 600 - 30 t -16 t² , b) v = -32 ft / s

c) v (1) = -62 ft / s,  v (3) = -126 ft / s , d) t = 7.13 s , e)  v = -258.16 ft / s

Explanation:

a) For this exercise they give us the function of the position of the ball

          s (t) = s (o) + v_o t - 16 t²

notice that you forgot to write the super index

indicate the initial position of the ball

        s (o) = 600 ft

also indicates initial speed

        v_o = - 30 ft / s

let's substitute in the equation

        s (t) = 600 - 30 t -16 t²

to find the speed we use

       v = ds / dt

       v = v_o - 32 t

       v = -30 - 32 t

b) To find the average speed, look for the speed at the beginning and end of the time interval

t = 1 s

     v (1) = -30 -32 1

     v (1) = - 62 ft / s

t = 3 s

     v (3) = -30 -32 3

     v (3) = -126 ft / s

the average speed is

    v = (v (3) -v (1)) / (3-1)

    v = (-126 +62) / 2

    v = -32 ft / s

c) instantaneous speeds, we already calculated them

    v (1) = -62 ft / s

    v (3) = -126 ft / s

d) the time to reach the ground

in this case s = 0

    0 = 600 - 30 t -16 t²

     t² + 1,875 t - 37.5 = 0

we solve the quadratic equation

     t = [-1,875 ±√ (1,875² + 4 37.5)] / 2

     t = [1,875 ± 12.39] / 2

     t₁ = 7.13 s

     t₂ = negative

Since the time must be positive, the correct answer is t = 7.13 s

e) the speed of the ball on reaching the ground

     v = -30 - 32 t

     v = -30 - 32 7.13

      v = -258.16 ft / s

Answer:

the magnitude is 7 and sign of the point charge on the surface shell is -13

Explanation:

Answer:

Explanation:

Sensorimotor Infants "think" by acting on the world with their eyes, ears, hands, and mouth.

Preoperational. Development of language and make-believe play takes place.

Concrete Operational children think in a logical, organized fashion only when dealing with concrete information they can perceive directly.

Formal Operational.  Adolescences  can also evaluate the logic of verbal statements without referring to real-world circumstances.

Sensorimotor, preoperational, concrete operational, and formal operational are Piaget's four phases of cognitive development.

The way youngsters think, investigate, and figure things out is referred to as cognitive development.

Piaget defined four stages of cognitive development:

1. Sensorimotor. From birth through the age of 18-24 months.

2. Preoperational.From infancy (18-24 months) until toddlerhood (age 7)

3. Operational concrete. 7 to 11 years old

4. Formal operational. From adolescence to adulthood

Hence, sensorimotor, preoperational, concrete operational, and formal operational are Piaget's four phases of cognitive development.

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Answer:

Explanation:

For a convex mirror, the value of its image distance and its focal length are negative.

using the mirror formula 1/f = 1/u+1/v

f is the focal length = Radius of curvature/2 = 0.560/2

f= 0.28m

u is the object distance = 10.6m

v is the position of the image = ?

On substitution;

1/0.28 = 1/10.6 + 1/-v

3.57 = 0.094 - 1/v

3.57 - 0.094 = -1/v

3.476 = -1/v

v = -1/3.476

v = -0.2877m

B) Since the image distance is negative, this means that the image is an upright and a virtual image. All Upright images has their image distance to be negative.

C) Magnification = Image distance/object distance

Magnification  = 0.2877/10.6

Magnification = 0.0271

Answer:

The classification of that same issue in question is characterized below.

Explanation:

The given values are:

Current, I = 50.0 A

Diameter, d = 0.10 cm

(a)...

As we know,

⇒  Magnetic force = Copper wire's weight

So,

⇒   [tex]B\times I\times L=M\times g[/tex]

On putting the estimated values, we get

⇒  [tex]B\times 50\times 1=7.037\times 10^{-3}\times 9.81[/tex]

⇒  [tex]50B=69.03297\times 10^{-3}[/tex]

⇒  [tex]B=1.38\times 10^{-3} \ T[/tex]

(b)...

As we know,

⇒  [tex]m=\delta\times L\times \frac{\pi \ d^2}{4}[/tex]

⇒      [tex]=8960\times 1\times \frac{\pi \ (0.001)^2}{4}[/tex]

⇒      [tex]=2240\times \pi \ 0.000001[/tex]

⇒      [tex]=7.037\times 10^{-3} \ kg[/tex]

Answer:

Explanation:

The kinetic energy possessed by the block when sliding will be equal to the energy needed to compress the string.

Kinetic energy = 1/2 mv² and energy stored in the spring = 1/2 ke²

m = mass of the block (in kg) = 2.8 kg

v = speed of the block (in m/s) = 2.4 m/s

k = force constant of the spring

e = extension (in metres) = 0.056m

Since KE = energy stored in the spring

1/2 mv² = 1/2 ke²

mv² = ke²

2.8(2.4)²  = k(0.056)²

16.128 = 0.003136k

k = 16.128/0.003136

k =  5,142.86

The force constant of the spring is 5,236.36

The force that constant of the spring is 5,142.86.

The kinetic energy that should be possessed by the block at the time when sliding will be equivalent to the energy required to compress the string.

Here

Kinetic energy = 1/2 mv² and energy stored in the spring = 1/2 ke²

m = mass of the block (in kg) = 2.8 kg

v = speed of the block (in m/s) = 2.4 m/s

k = force constant of the spring

e = extension (in metres) = 0.056m

Since KE = energy stored in the spring

So,

1/2 mv² = 1/2 ke²

mv² = ke²

Now

2.8(2.4)²  = k(0.056)²

16.128 = 0.003136k

k = 16.128/0.003136

k =  5,142.86

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Answer:

The answer is option 2.

Explanation:

Both sides are pulling the rope with equal force where the rope doesn't move. So they have a balanced forces.

Answer

The rate at which the magnetic field is changing is  [tex][\frac{dB}{dt} ] = 0.000467 T/s[/tex]

Explanation

From the question we are told that

   The electric field strength is [tex]E = 3.5mV/m = 3.5 *10^{-3} \ V/m[/tex]

    The radius is  [tex]r = 1.5 \ m[/tex]

The rate of change of the  magnetic  field  is mathematically represented as

        [tex]\frac{d \phi }{dt} = \int\limits^{} {E \cdot dl}[/tex]

Where [tex]dl[/tex] is change of a unit length

     [tex]\frac{d \phi}{dt} = A * \frac{dB}{dt}[/tex]

Where A is the area which is mathematically represented as

     [tex]A = \pi r^2[/tex]

    So

    [tex]E \int\limits^{} { dl} = ( \pi r^2) (\frac{dB}{dt} )[/tex]  

  [tex]E L = ( \pi r^2) (\frac{dB}{dt} )[/tex]  

where L is the circumference of the circle which is mathematically represented as

     [tex]L = 2 \pi r[/tex]

So

     [tex]E (2 \pi r ) = (\pi r^2 ) [\frac{dB}{dt} ][/tex]

      [tex]E = \frac{r}{2} [\frac{dB}{dt} ][/tex]

       [tex][\frac{dB}{dt} ] = \frac{E}{ \frac{r}{2} }[/tex]

substituting values

      [tex][\frac{dB}{dt} ] = \frac{3.5 *10^{-3}}{ \frac{15}{2} }[/tex]

      [tex][\frac{dB}{dt} ] = 0.000467 T/s[/tex]    

Before the bus starts moving, the bus and the skater are both standing still.

When the bus starts moving and pulls away from the bus-stop, the skater stays right where she is.  

The people outside on the sidewalk see her standing still, and they see the bus moving out from under her.  

The other passengers on the bus see her rolling backwards down the aisle, toward the back of the bus.

Answer:

Work is done by friction = -165 J

Explanation:

Given:

Mass of block (m) = 15 kg

Ramp inclined = 28°

Friction force (f) = 30 N

Distance (d) = 5.5 m

Find:

Work is done by friction.

Computation:

Work is done by friction = -Fd

Work is done by friction = -(30)(5.5)

Work is done by friction = -165 J

Answer:

The thermal power emitted by the body is [tex]P_t = 286.8 \ Wm^{-2}[/tex]

The net power radiated is  [tex]P_{net} = 460 \ W[/tex]

Explanation:

From the question we are told that

   The length of the assumed hum[tex]T_{room} = 20 ^oC[/tex]an body is  L =  2.0 m

   The circumference of the assumed human body is  [tex]C = 0.8 \ m[/tex]

   The  Stefan-Boltzmann constant is  [tex]\sigma = 5.67 * 10^{-8 } \ W\cdot m^{-2} \cdot K^{-4}.[/tex]

    The temperature of skin [tex]T_{body} = 30^oC[/tex]

     The temperature of the room is  

    The emissivity is  e=0.6

The thermal power radiated by the body is mathematically represented as

           [tex]P_t = e * \sigma * T_{body}^4[/tex]

substituting value

        [tex]P_t = 0.6 * 5.67*10^{-8} * (303)^4[/tex]

        [tex]P_t = 286.8 \ Wm^{-2}[/tex]

The net power radiated by the body is mathematically evaluated as

    [tex]P_{net} = P_t * A[/tex]

Where A is the surface area of the body which is mathematically evaluated as

     [tex]A = C* L[/tex]

substituting values

      [tex]A = 0.8 * 2[/tex]

      [tex]A = 1.6 m^2[/tex]

=>    [tex]P_{net} = 286.8 * 1.6[/tex]

=>   [tex]P_{net} = 460 \ W[/tex]

Answer:

11.8 Joules

Explanation:

Given:-

- The height of the target ball, si = 0.860 m

- The mass of target and steel ball, m = 0.012 kg

- The target ball travels a distance ( x ) after being struck = 1.40 m

Find:-

What is the kinetic energy (in joules) of the target ball just after it is struck?

Solution:-

- We are given the initial distance of the target ball as 0.86 m above the floor which travels a distance ( x ) after being struck.

- We will employ the one dimensional kinematic equation of motion to determine the initial velocity ( vi ) of the target ball as follows:

                        [tex]vf^2 = vi^2 - 2*g*x[/tex]

Where,

                  vf: The final velocity of target ball at maximum height = 0

                  g: The gravitational acceleration constant = 9.8 m/s^2

- Plug in the required parameters and evaluate the ( vi ) as follows:

                      [tex]0^2 = vi^2 - 2*( 9.80 )*( 1.40 )\\\\vi^2 = 27.44\\\\vi = \sqrt{27.44} = 5.24 m/s[/tex]

- The kinetic energy ( Ek ) of an object with mass ( m ) and initial velocity ( vi ) is expressed as:

                       [tex]E_k = 0.5*m*(vi)^2\\\\E_k = 0.5*0.86*27.44\\\\E_k = 11.8 J[/tex]

Answer: The kinetic energy of the target ball just after it is struck is 11.8 Joules.

Answer:

C

Explanation:

The intermolecular forces between the water molecule is less binding than that of the copper molecule. Hence the water would take a shorter time to be converted to vapour where the temperature of boiling is constant however the temperature of that of the copper molecule keeps increasing.

Answer:

C) less than 129 lb.

Explanation:

Let the elevator be slowing up with magnitude of a . That means it is accelerating downwards  with magnitude a .

If R be the reaction force

For the elevator is going downwards with acceleration a

mg - R = ma

R = mg - ma

R measures its apparent weight . Spring scale will measure his apparent weight.

So its apparent weight is less than 129 lb .

Answer:

The minimum angular spread of the laser beam is 3.32 × [tex]10^{-6}[/tex] radians (or 3.32 μrad).

Explanation:

The minimum angular spread of a wave is the ratio of its narrowest diameter to its wavelength.

From Rayleigh's formula,

Angular spread = 1.22 (wavelength ÷ diameter)

                          = 1.22 (λ ÷ D)

Given that:

diameter, D = 0.18 m and wavelength, λ = 490 nm, then;

Angular spread of the laser beam = 1.22 (λ ÷ D)

                         = 1.22[tex](\frac{490*10^{-9} }{0.18})[/tex]

                         = 1.22× 2.7222 × [tex]10^{-6}[/tex]

                        = 3.3211 × [tex]10^{-6}[/tex] rad

The minimum angular spread of the laser beam is 3.32 × [tex]10^{-6}[/tex] radians.

Answer:

Explanation:

During the swing , the center of mass will go down due to which disc will lose potential energy which will be converted into rotational kinetic energy

mgh = 1/2 I ω² where m is mass of the disc , h is height by which c.m goes down which will be equal to radius of disc , I is moment of inertia of disc about the nail at rim , ω is angular velocity .

mgr  = 1/2 x ( 1/2 m r²+ mr²) x ω²

gr  = 1/2 x 1/2  r² x ω² + 1/2r² x ω²

g = 1 / 4 x ω² r + 1 / 2 x ω² r

g = 3  x ω² r/ 4

ω² = 4g /3 r

= 4 x 9.8 /  3 x  .25

= 52.26

ω = 7.23  rad / s .

Answer:

B. At the instant when the block is at the highest point, directed at the block.

Explanation:

Motion of an object is the change in the position of the object with respect to time. On the earth, gravity has a great influence on the motion of an object (especially in a vertical direction).

When the block is projected up in the air, it moves with a varying velocity until the velocity becomes zero due to gravity. Which make the object to rest a little in the air (when velocity = gravity) and starts to fall freely.

To ensure hitting the block by the ball, it is thrown at the block when the block is at its highest point in the air. Since the block would be at rest at this instant before it start to fall at a constant acceleration under gravity.

Answer:

A) Fb = 671.3 N

B) The diver will sink.

Explanation:

A)

The buoyant force applied on an object by a fluid is given by the following formula:

Fb = Vρg

where,

Fb = Buoyant Force = ?

V = Volume of the water displaced by the object = 68.5 L = 0.0685 m³

ρ = Density of Water = 1000 kg/m³

g = 9.8 m/s²

Therefore,

Fb = (0.0685 m³)(1000 kg/m³)(9.8 m/s²)

Fb = 671.3 N

B)

Now, in order to find out whether the diver sinks or float, we need to find weight of the diver with gear.

W = mg = (71.8 kg)(9.8 m/s²)

W = 703.64 N

Since, W > Fb. Therefore, the downward force of weight will make the diver sink.

The diver will sink.

Answer:

A. 2.82 eV

B. 439nm

C. 59.5 angstroms

Explanation:

A. To calculate the energy of the photon emitted you use the following formula:

[tex]E_{n1,n2}=-13.4(\frac{1}{n_2^2}-\frac{1}{n_1^2})[/tex]     (1)

n1: final state = 5

n2: initial state = 2

Where the energy is electron volts. You replace the values of n1 and n2 in the equation (1):

[tex]E_{5,2}=-13.6(\frac{1}{5^2}-\frac{1}{2^2})=2.82eV[/tex]

B. The energy of the emitted photon is given by the following formula:

[tex]E=h\frac{c}{\lambda}[/tex]   (2)

h: Planck's constant = 6.62*10^{-34} kgm^2/s

c: speed of light = 3*10^8 m/s

λ: wavelength of the photon

You first convert the energy from eV to J:

[tex]2.82eV*\frac{1J}{6.242*10^{18}eV}=4.517*10^{-19}J[/tex]

Next, you use the equation (2) and solve for λ:

[tex]\lambda=\frac{hc}{E}=\frac{(6.62*10^{-34} kg m^2/s)(3*10^8m/s)}{4.517*10^{-19}J}=4.39*10^{-7}m=439*10^{-9}m=439nm[/tex]

C. The radius of the orbit is given by:

[tex]r_n=n^2a_o[/tex]   (3)

where ao is the Bohr's radius = 2.380 Angstroms

You use the equation (3) with n=5:

[tex]r_5=5^2(2.380)=59.5[/tex]

hence, the radius of the atom in its 5-th state is 59.5 anstrongs

A) The energy E of the emitted photon in electron volts is; E = 2.856 eV

B) The wavelength in nanometers of the emitted photon is; λ = 434.4nm

C) The radius of the hydrogen atom in nanometers in its initial 5th energy level is; rₙ = 1.323 nm

A) Formula for the energy E of the emitted photons is;

E = -13.6([tex]\frac{1}{n_{2}^2} - \frac{1}{n_{1}^2}[/tex])

We are given;

n₂ = 5

n₁ = 2

Thus;

E = -13.6([tex]\frac{1}{5^2} - \frac{1}{2^2}[/tex])

E = 2.856 eV

B) The formula for the wavelength is;

λ = hc/E

where;

h is Planck's constant = 6.626 × 10⁻³⁴ m².kg/s

c is speed of light = 3 × 10⁸ m/s

E is energy of photon

λ is wavelength of the photon

Earlier we saw that E = 2.856 eV. Converting to Joules gives;

E = 4.5758 × 10⁻¹⁹ J

Thus;

λ = (6.626 × 10⁻³⁴ × 3 × 10⁸)/(4.5758 × 10⁻¹⁹)

λ = 4.344 × 10⁻⁷ m

Converting to nm gives;

λ = 434.4nm

C) Formula for the radius of the hydrogen atom is;

rₙ = n²a₀

where;

a₀ is bohr's radius = 5.292 × 10⁻¹¹ m

n = 5

Thus;

rₙ = 5² × 5.292 × 10⁻¹¹

rₙ = 1.323 × 10⁻⁹

rₙ = 1.323 nm

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