Question

(A) Calculate the wavelength (in nm) of light with energy 1.89 × 10–20 J per photon, (b) For light of wavelength 410 nm, calculate the number of photons per joule, (c) Determine the binding energy (in eV) of a metal if the kinetic energy possessed by an ejected electron [using one of the photons in part (b)] is 2.93 × 10–19 J.

Answer 1

Answer:

For A: The wavelength of the light is $1.052\times 10^4nm$

For B: The number of photons per joule is $2.063\times 10^{18}$

For C: The binding energy of a metal is 1.197 eV.

Explanation:

The equation used to calculate the energy of a photon follows:

$E=\frac{hc}{\lambda}$            ......(1)

where,

E = energy of a photon

h = Planck's constant = $6.626\times 10^{-34}J.s$

c = speed of light = $3\times 10^{8}m/s$

$\lambda$ = wavelength

• For A:

Given values:

E = $1.89\times 10^{-20}J$

Putting values in equation 1, we get:

$\lambda=\frac{(6.626\times 10^{-34}J.s)\times (3\times 10^8m/s)}{1.89\times 10^{-20}J}\\\\\lambda=1.052\times 10^{-5}m$

Converting the wavelength into nanometers, the conversion factor used is:

$1m=10^9nm$

So, $\lambda=1.052\times 10^{-5}m\times \frac{10^9nm}{1m}=1.052\times 10^4nm$

Hence, the wavelength of the light is $1.052\times 10^4nm$

• For B:

Given values:

$\lambda=410nm=410\times 10^{-9}m$

Putting values in equation 1, we get:

$E=\frac{(6.626\times 10^{-34}J.s)\times (3\times 10^8m/s)}{410\times 10^{-9}m}\\\\E=4.848\times 10^{-19}J$

To calculate the number of photons, we use the equation:

$\text{Number of photons}=\frac{\text{Total energy}}{\text{Energy of a photon}}$

Total energy = 1 J

Energy of a photon = $4.848\times 10^{-19}J$

Putting values in the above equation:

$\text{Number of photons}=\frac{1J}{4.848\times 10^{-19}J}\\\\\text{Number of photons}=2.063\times 10^{18}$

Hence, the number of photons per joule is $2.063\times 10^{18}$

• For C:

To calculate the binding energy of a metal, we use the equation:

$E=K+B$             .....(2)

E = Total energy

K = Kinetic energy of a photon

B = Binding energy of metal

Converting the energy from joules to eV, the conversion factor used is:

$1eV=1.602\times 10^{-19}J$

Using the above conversion factor:

$K=2.93\times 10^{-19}J=1.829eV\\\\E=4.848\times 10^{-19}J=3.026eV$

Putting values in equation 2:

$B=(3.026-1.829)eV=1.197eV$

Hence, the binding energy of a metal is 1.197 eV.