Question

When the tube is filled with mercury vapor, as in this case, a sharp drop in the collected current is observed when the accelerating potential reaches 4.9 . The current drops suddenly to a negligible value and slowly increases again when the accelerating potential is above 4.9 . What is the energy absorbed by the atomic electrons in the mercury atom when the accelerating potential is 4.9 ?
B) The excited mercury atoms decay back to the lowest energy level by emitting radiation. What is the wavelength of this radiation?

Answer 1

Answer:

253.54 nm

Explanation:

h = Planck's constant = $6.626\times 10^{-34}\ m^2kg/s$

c = Speed of light = $3\times 10^8\ m/s$

$\lambda$ = Wavelength

V = Voltage = 4.9 V

The loss in kinetic energy = Gain in potential energy (energy conservation)

$E=eV\\\Rightarrow E=1.6\times 10^{-19}\times 4.9\\\Rightarrow E=7.84\times 10^{-19}\ J$

Energy is given by

$E=\dfrac{hc}{\lambda}\\\Rightarrow \lambda=\dfrac{hc}{E}\\\Rightarrow \lambda=\dfrac{6.626\times 10^{-34}\times 3\times 10^{8}}{7.84\times 10^{-19}}\\\Rightarrow \lambda=2.53546\times 10^{-7}=253.54\ nm$

The wavelength is 253.54 nm