Question

6. Franck-Hertz experiment. Mercury vapor is used in a Franck-Hertz experiment. You get the following data: 400 Franck-Hertz Dato for Mercury 300 4 100 10 15 Accelereting Voltage From this graph, estimate the wavelength of a photon emitted when an electron in the first excited state of Hg jumps to the ground state.

Answer 1

When electrons are accelerated in the Franck-Hertz apparatus, the collected current rises with accelerated voltage. As the graph shows that when the accelerating voltage reaches 4.9 volts, the current sharply drops, which indicates the beginning of a new phenomenon. This drop is attributed to inelastic collisions between the accelerated electrons and atomic electrons in the mercury atoms. The sudden onset suggests that the mercury electrons cannot accept energy until it reaches the threshold for elevating them to an excited state. This 4.9 volt excited state corresponds to a strong line in the ultraviolet emission spectrum of mercury at 254 nm (a 4.9eV photon). The wavelength of an electron is dependent upon accelerating voltage and is given by:

When electrons are accelerated in the Franck-Hertz apparatus, the collected current rises with accelerated voltage. As the graph shows that when the accelerating voltage reaches 4.9 volts, the current sharply drops, which indicates the beginning of a new phenomenon. This drop is attributed to inelastic collisions between the accelerated electrons and atomic electrons in the mercury atoms. The sudden onset suggests that the mercury electrons cannot accept energy until it reaches the threshold for elevating them to an excited state. This 4.9 volt excited state corresponds to a strong line in the ultraviolet emission spectrum of mercury at 254 nm (a 4.9eV photon). The wavelength of an electron is dependent upon accelerating voltage and is given by: lambda = h/squareroot 2meV where

where

h	Planck’s constant (6.626 x 10-34 J s)
m	electron mass (9.109 x 10-31 kg)
e	electronic charge (1.60 x 10-19 C)
V	accelerating voltage (V)