Question 379: Dual Nature of Matter and Radiation

Question

A metal surface is illuminated with photons of energies $E_1=4 \mathrm{eV}$ and $E_2=2.5 \mathrm{eV}$ respectively. The ratio of maximum speeds of the photoelectrons in two cases is 2 .
Work function of metal surface will be

Accepted Answer

To find the work function of the metal surface, we can use Einstein's photoelectric equation, which is given by:
$ 	ext{KE} = h f - \phi_0 $
where KE is the kinetic energy of the emitted photoelectron, $h f$ is the energy of the incident photon, and $\phi_0$ is the work function of the metal.
For the two photon energies provided, we have:
For photon energy $E_1 = 4 	ext{ eV}$:
$ \frac{1}{2} m v_1^2 = 4 - \phi_0 \quad 	ext{........ (i)} $
For photon energy $E_2 = 2.5 	ext{ eV}$:
$ \frac{1}{2} m v_2^2 = 2.5 - \phi_0 \quad 	ext{........ (ii)} $
Given that the ratio of the maximum speeds of the photoelectrons in the two cases is 2, we can express:
$ \frac{v_1^2}{v_2^2} = \frac{4 - \phi_0}{2.5 - \phi_0} $
Since $\frac{v_1}{v_2} = 2$, this implies:
$ 4 = \frac{4 - \phi_0}{2.5 - \phi_0} $
Solving the equation:
$ 4(2.5 - \phi_0) = 4 - \phi_0 $
Expanding and simplifying gives:
$ 10 - 4\phi_0 = 4 - \phi_0 $
Rearranging the terms results in:
$ 10 - 4 = 3\phi_0 $
$ \phi_0 = 2 	ext{ eV} $
Thus, the work function of the metal surface is $2 	ext{ eV}$.

Answer

2.5 eV

Answer

5 eV

Answer

4 eV

Answer

2 eV

Dual Nature of Matter and Radiation

A metal surface is illuminated with photons of energies E_1=4 \mathrm{eV} and E_2=2.5 \mathrm{eV} respectively. The ratio of maximum speeds of the photoelectrons in two cases is 2 . Work function of metal surface will be

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