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

For A: The wavelength of the light is
`1.052* 10^4nm`

For B: The number of photons per joule is
`2.063* 10^(18)`

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

Step-by-step explanation:

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

`E=(hc)/(\lambda)` ......(1)

where,

E = energy of a photon

h = Planck's constant =
`6.626* 10^(-34)J.s`

c = speed of light =
`3* 10^(8)m/s`

`\lambda` = wavelength

• For A:

Given values:

E =
`1.89* 10^(-20)J`

Putting values in equation 1, we get:

`\lambda=((6.626* 10^(-34)J.s)* (3* 10^8m/s))/(1.89* 10^(-20)J)\\\\\lambda=1.052* 10^(-5)m`

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

`1m=10^9nm`

So,
`\lambda=1.052* 10^(-5)m* (10^9nm)/(1m)=1.052* 10^4nm`

Hence, the wavelength of the light is
`1.052* 10^4nm`

• For B:

Given values:

`\lambda=410nm=410* 10^(-9)m`

Putting values in equation 1, we get:

`E=((6.626* 10^(-34)J.s)* (3* 10^8m/s))/(410* 10^(-9)m)\\\\E=4.848* 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* 10^(-19)J`

Putting values in the above equation:

`\text{Number of photons}=(1J)/(4.848* 10^(-19)J)\\\\\text{Number of photons}=2.063* 10^(18)`

Hence, the number of photons per joule is
`2.063* 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* 10^(-19)J`

Using the above conversion factor:

`K=2.93* 10^(-19)J=1.829eV\\\\E=4.848* 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.