Ultraviolet light of wavelength $2271 \circ A$ from a $100 W$ mercury source irradiates a photocell made of molybdenum metal. If the stopping potential is $- 1.3 V$ , estimate the work function of the metal. How would the photocell respond to a high intensity $(\sim 10^{5} W / m^{2})$ red light of wavelength $6328 \circ A$ produced by a He-Ne laser?

Open in App

Solution

Step 1: Find the work function.
Formula used: $ϕ_{0} = h v - e V_{0}$
Given:
Wavelength of ultraviolet light,
$λ = 2271 \circ A$
$λ = 2271 \times 10^{- 10} m$
Stopping potential of the metal, $V_{0} = 1.3 V$
Planck's constant, $h = 6.6 \times 10^{- 34} J s$
Charge on an electron, $e = 1.6 \times 10^{- 19} C$
Wavelength of red light,
$λ_{R} = 6328 \circ A = 6328 \times 10^{- 10} m$
If the work function of the metal is $ϕ$ and the frequency of incident radiation is v,
Then Work function is given by: $ϕ_{0} = h v - e V_{0}$
$ϕ_{0} = \frac{h c}{λ} - e V_{0}$
$ϕ_{0} = \frac{6.63 \times 10^{- 34} \times 3 \times 10^{8}}{2271 \times 10^{- 10}} - 1.6 \times 10^{- 19} \times 1.3$
$ϕ_{0} \approx 8.75 \times 10^{- 19} - 2.08 \times 10^{- 19}$
$ϕ_{0} \approx 6.7 \times 10^{- 19} J$
$ϕ$ in electron volt (eV)
$= \frac{6.7 \times 10^{- 19}}{1.6 \times 10^{- 19}} e V$
$ϕ_{0} = 4.2 e V$
Step 2 : Find the theshold frequency.
Formula used : $ϕ_{0} = h v_{0}$
Let $v_{0}$ be the threshold frequency of the metal, then, we have,
$ϕ_{0} = h v_{0}$
$v_{0} = \frac{ϕ_{0}}{h}$
$v_{0} = \frac{6.7 \times 10^{- 19}}{6.63 \times 10^{- 34}}$
$v_{0} = 1.01 \times 10^{15} Hz$
Step 3: Find the frequency of red light.
Formula used: $v_{R} = \frac{c}{λ_{R}}$
Now frequency of red light
$v_{R} = \frac{c}{λ_{R}}$
$v_{R} = \frac{3 \times 10^{8}}{6328 \times 10^{- 10}}$
$v_{R} \approx 4.74 \times 10^{14} Hz$
Since $v_{0} > v_{r}$ , the photo - cell will not respond
howsoever high be the intensity of laser light.
Final Answer : $ϕ_{0} = 4.2 e V$
$v_{0} \approx 1 \times 10^{15} Hz$
$v_{R} \approx 4.74 \times 10^{14} Hz$

Suggest Corrections

Similar questions

Ultraviolet light of wavelength 2271 Å from a 100 W mercury source irradiates a photo-cell made of molybdenum metal. If the stopping potential is −1.3 V, estimate the work function of the metal. How would the photo-cell respond to a high intensity (∼10⁵ W m⁻²) red light of wavelength 6328 Å produced by a He-Ne laser?

Q. Ultraviolet light of wavelength