(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.

For A: The wavelength of the light is

For B: The number of photons per joule is

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

Explanation:

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

           ......(1)

where,

E = energy of a photon

h = Planck's constant =

c = speed of light =

= wavelength

Given values:

E =

Putting values in equation 1, we get:

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

So,

Hence, the wavelength of the light is

Given values:

Putting values in equation 1, we get:

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

Total energy = 1 J

Energy of a photon =

Putting values in the above equation:

Hence, the number of photons per joule is

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

            .....(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:

Using the above conversion factor:

Putting values in equation 2:

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

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