Answered: A silver ball of radius 4"8 cm is…

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Question

A silver ball of radius 4"8 cm is suspended by a thread in a vacuum chamber. Ultraviolet light of wavelength 200 nm is incident on the ball for some time during which a total light energy of 1.0 x 10^-11 J falls on the surface. Assuming that on the average one photon out of every ten thousand is able to eject a photoelectron, find the electric potential at the surface of the ball assuming zero potential at infinity. What is the potential at the centre of the ball?

Expert Solution

Step 1

Given:

The radius of ball is $r = 4.8 cm$ .
The wavelength of light is $λ = 200 nm$ .
The total energy of light is $E = 1.0 \times 10^{- 11} J$ .
The number of photon ejected is $n = 10000$ .

The formula to calculate the energy of one photon of light is,

$E_{0} = \frac{h c}{λ}$

Here, E₀ is the energy of one photon, h is the Planck's constant, c is the speed of light and $λ$ is the wavelength of light.

Substitute the known values in the formula to calculate the energy of one photon.

$\begin{array}{rcl} E_{0} & = & \frac{(6.626 \times 10^{- 34} J \cdot s) (3 \times 10^{8} m / s)}{(200 nm) (\frac{10^{- 9} m}{1 nm})} \\ = & 9.94 \times 10^{- 19} J \end{array}$

Step 2

The formula to calculate the total number of photons emitted by light is,

$N = \frac{E}{E_{0}}$

Here, N is the total number of photons and E is the total energy emitted by light.

Substitute the known values in the formula to calculate the total number of photons emitted by light.

$\begin{array}{rcl} N & = & \frac{1.0 \times 10^{- 11} J}{9.94 \times 10^{- 19} J} \\ = & 1.01 \times 10^{7} \end{array}$

The formula to calculate the number of photoelectrons of light is,

$n_{e} = \frac{N}{n}$

Here, n_e is the number of photo electrons and n is the number of photons ejected.

Substitute the known values in the formula to calculate the number of photoelectrons.

$\begin{array}{rcl} n_{e} & = & \frac{1.01 \times 10^{7}}{10000} \\ = & 1.01 \times 10^{3} \end{array}$

The formula to calculate the total charge of electrons emitted by light is,

$q = n_{e} e$

Here, q is the total charge of electrons and e is the basic charge of electron.

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