Question

Calculate the frequency of the radiation required to eject photoelectrons to a velocity of 9 X105 MS-1 from sodium metal surface, having a threshold frequency of 4.61 x 1014 Hz (mass of photoelectron = 9.109 x 10 -31 kg).

Answer 1

Answer on Question #48949 – Chemistry – Inorganic Chemistry

Question:

Calculate the frequency of the radiation required to eject photoelectrons to a velocity of $9 \times 10^{5} \, \text{MS}^{-1}$ from sodium metal surface, having a threshold frequency of $4.61 \times 10^{14} \, \text{Hz}$ (mass of photoelectron = $9.109 \times 10^{-31} \, \text{kg}$)

Solution:

According to Einstein’s equation energy of photon (irradiation energy) is given by

$$h\nu = m \times \nu^{2}/2 + A$$

where $\nu$ – the irradiation frequency, $\nu$ – the velocity of photo electrons, $A$ – the work function and $h = 6.62606957 \times 10^{-34} \, \text{J s}$.

The work function can be calculated using the threshold frequency $(v_0)$ when $V = 0$:

$$A = h\nu_0$$

Thus, $v = (m \times \nu^{2}/2 + h\nu_0)/h$

$$\begin{aligned} v &= (9.109 \times 10^{-31} \, \text{kg} \times 40.5 \times 10^{10} \, \text{m}^2/\text{s}^2)/(6.62606957 \times 10^{-34} \, \text{J s}) + 4.61 \times 10^{14} \, \text{Hz} = \\ &= 5.56762 \times 10^{14} \, \text{Hz} + 4.61 \times 10^{14} \, \text{Hz} = 10.17762 \, \text{Hz} \end{aligned}$$

Answer: 10.17762 Hz

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