When UV light of wavelength 295nm falls on a metal surface, the maximum kinetic energy of emitted electrons is 1.50eV.
What is the work function of the metal?
W0 in eV
Please someone help me out. Thank you.
To find the work function of the metal, we can make use of the relationship between the energy of a photon and the work function.
The energy of a photon (E) is given by the equation:
E = hc/λ
Where:
- E is the energy of the photon
- h is Planck's constant (6.626 x 10^-34 Js)
- c is the speed of light (3.0 x 10^8 m/s)
- λ is the wavelength of the light
In this case, the energy of the photon is equal to the maximum kinetic energy of the emitted electrons:
E = 1.50 eV (1)
The work function (W0) is the minimum energy required to remove an electron from the metal.
Now, let's convert 295 nm to meters:
λ = 295 nm = 295 x 10^-9 m
Substituting all the values into the equation, we have:
1.50 eV = (6.626 x 10^-34 Js)(3.0 x 10^8 m/s) / (295 x 10^-9 m)
Now, we can solve for the work function (W0):
W0 = [(1.50 eV)(295 x 10^-9 m)] / (6.626 x 10^-34 Js)(3.0 x 10^8 m/s)
Simplifying the equation gives:
W0 = 4.77 eV
Therefore, the work function of the metal is 4.77 eV.