Question

If the two metals $A$ and $B$ are exposed to radiation of wavelength $350 mm$. The work functions of metals $A$ and $B$ are $4.8 eV$ and $2.2 eV$. Then choose the correct option

• A. Both metals A and B will emit photo-electrons
• B. Metal B will not emit photo-electrons
• C. Both metals $A$ and $B$ will not emit photo-electrons
• D. Metal A will not emit photo-electrons

Hint:

For photoelectric emission to occur, the photon energy must be greater than the work function of the material.

Answer 1

The Correct Option is D

To determine whether metals \(A\) and \(B\) will emit photoelectrons when exposed to radiation, we need to use the photoelectric effect principle. According to this principle, photoelectrons are emitted from a metal surface if the energy of the incident photons is greater than the work function of the metal.

The energy of the incident photons is given by the equation:

\(E = \frac{hc}{\lambda}\)

Where:

• \(h\) is the Planck's constant \( (6.626 \times 10^{-34}\, \text{J s}) \).
• \(c\) is the speed of light in vacuum \( (3 \times 10^{8}\, \text{m/s}) \).
• \(\lambda\) is the wavelength of the incident radiation \( (350\, \text{nm} = 350 \times 10^{-9}\, \text{m}) \).

Converting wavelength to meters:

\(\lambda = 350 \times 10^{-9}\, \text{m}\)

Converting the energy from Joules to electron volts (1 eV = \(1.602 \times 10^{-19}\) J):

Substitute the values into the energy equation:

\(E = \frac{(6.626 \times 10^{-34})(3 \times 10^{8})}{350 \times 10^{-9}}\)

After calculation:

\(E = 5.68 \times 10^{-19}\, \text{J}\)

Convert this energy into electron volts:

\(E = \frac{5.68 \times 10^{-19}}{1.602 \times 10^{-19}} = 3.55 \, \text{eV}\)

We now compare this energy to the work functions of metals \(A\) and \(B\):

• Work function of metal \(A\) = \(4.8\, \text{eV}\)
• Work function of metal \(B\) = \(2.2\, \text{eV}\)

Conclusion:

• Since \(3.55 \, \text{eV} < 4.8 \, \text{eV}\), metal \(A\) will not emit photoelectrons.
• Since \(3.55 \, \text{eV} > 2.2 \, \text{eV}\), metal \(B\) will emit photoelectrons.

Therefore, the correct option is: Metal A will not emit photo-electrons.