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
To find the work function (W0) of the metal, we need to use the equation:
Kinetic energy (KE) = Photon energy (E) - Work function (W0)
Since we are given the maximum kinetic energy of the emitted electrons, we can use this value to find the work function.
First, convert the given wavelength of UV light into energy using the equation:
E = hc/λ
Where:
- E is the energy of a single photon
- h is Planck's constant (6.626 x 10^-34 J·s or 4.135 x 10^-15 eV·s)
- c is the speed of light (3.00 x 10^8 m/s)
- λ is the wavelength of the UV light (295 nm or 295 x 10^-9 m)
Substituting the values into the equation:
E = (6.626 x 10^-34 J·s * 3.00 x 10^8 m/s) / (295 x 10^-9 m)
E ≈ 6.68 x 10^-19 J
Since we need the energy in electron volts (eV), we can convert it by dividing by the conversion factor:
1 eV = 1.602 x 10^-19 J
E ≈ (6.68 x 10^-19 J) / (1.602 x 10^-19 J/eV)
E ≈ 4.17 eV
Now, we can substitute this value for the photon energy into the equation for kinetic energy:
KE = E - W0
We know that the maximum kinetic energy (KE) is given as 1.50 eV. Substituting this value, we get:
1.50 eV = 4.17 eV - W0
Now, rearrange the equation to solve for the work function (W0):
W0 = 4.17 eV - 1.50 eV
W0 ≈ 2.67 eV
Therefore, the work function (W0) of the metal is approximately 2.67 eV.