Respuesta :
Answer:
For A: The wavelength of the light is [tex]1.052\times 10^4nm[/tex]
For B: The number of photons per joule is [tex]2.063\times 10^{18}[/tex]
For C: The binding energy of a metal is 1.197 eV.
Explanation:
The equation used to calculate the energy of a photon follows:
[tex]E=\frac{hc}{\lambda}[/tex] ......(1)
where,
E = energy of a photon
h = Planck's constant = [tex]6.626\times 10^{-34}J.s[/tex]
c = speed of light = [tex]3\times 10^{8}m/s[/tex]
[tex]\lambda[/tex] = wavelength
- For A:
Given values:
E = [tex]1.89\times 10^{-20}J[/tex]
Putting values in equation 1, we get:
[tex]\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[/tex]
Converting the wavelength into nanometers, the conversion factor used is:
[tex]1m=10^9nm[/tex]
So, [tex]\lambda=1.052\times 10^{-5}m\times \frac{10^9nm}{1m}=1.052\times 10^4nm[/tex]
Hence, the wavelength of the light is [tex]1.052\times 10^4nm[/tex]
- For B:
Given values:
[tex]\lambda=410nm=410\times 10^{-9}m[/tex]
Putting values in equation 1, we get:
[tex]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[/tex]
To calculate the number of photons, we use the equation:
[tex]\text{Number of photons}=\frac{\text{Total energy}}{\text{Energy of a photon}}[/tex]
Total energy = 1 J
Energy of a photon = [tex]4.848\times 10^{-19}J[/tex]
Putting values in the above equation:
[tex]\text{Number of photons}=\frac{1J}{4.848\times 10^{-19}J}\\\\\text{Number of photons}=2.063\times 10^{18}[/tex]
Hence, the number of photons per joule is [tex]2.063\times 10^{18}[/tex]
- For C:
To calculate the binding energy of a metal, we use the equation:
[tex]E=K+B[/tex] .....(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:
[tex]1eV=1.602\times 10^{-19}J[/tex]
Using the above conversion factor:
[tex]K=2.93\times 10^{-19}J=1.829eV\\\\E=4.848\times 10^{-19}J=3.026eV[/tex]
Putting values in equation 2:
[tex]B=(3.026-1.829)eV=1.197eV[/tex]
Hence, the binding energy of a metal is 1.197 eV.
