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

253.54 nm

Step-by-step explanation:

h = Planck's constant =
`6.626* 10^(-34)\ m^2kg/s`

c = Speed of light =
`3* 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* 10^(-19)* 4.9\\\Rightarrow E=7.84* 10^(-19)\ J`

Energy is given by

`E=(hc)/(\lambda)\\\Rightarrow \lambda=(hc)/(E)\\\Rightarrow \lambda=(6.626* 10^(-34)* 3* 10^(8))/(7.84* 10^(-19))\\\Rightarrow \lambda=2.53546* 10^(-7)=253.54\ nm`

The wavelength is 253.54 nm