Question

A mercury lamp is a convenient source for studying frequency dependence of photoelectric emission, since it gives a number of spectral lines ranging from the UV to the red end of the visible spectrum. In our experiment with rubidium photo-cell, the following lines from a mercury source were used: λ1 = 3650 Å, λ₂= 4047 Å, λ₃= 4358 Å, λ₄= 5461 Å, λ5= 6907 Å, The stopping voltages, respectively, were measured to be: V01 = 1.28 V, V₀₂ = 0.95 V, V₀₃ = 0.74 V, V₀₄ = 0.16 V, V₀₅ = 0 V

  Determine the value of Planck’s constant h, the threshold frequency and work function for the material.
[Note:

 You will notice that to get h from the data, you will need to know e (which you can take to be 1.6 × 10⁻¹⁹ C). Experiments of this kind on Na, Li, K, etc. were performed by Millikan, who, using his own value of e (from the oil-drop experiment) confirmed Einstein’s photoelectric equation and at the same time gave an independent estimate of the value of h.]

Answer 1

Einstein’s photoelectric equation is given as:

Where,
V0 = Stopping potential
h = Planck’s constant
e = Charge on an electron
ν = Frequency of radiation

This relation can be used to obtain the frequencies of the various lines of the given
wavelengths.

The given quantities can be listed in tabular form as:

Frequency × 1014 Hz	8.219	7.412	6.884	5.493	4.343
Stopping potential V0	1.28	0.95	0.74	0.16	0

The following figure shows a graph between ν and V_0.

It can be observed that the obtained curve is a straight line. It intersects the ν-axis at 5×10¹⁴ Hz, which is the threshold frequency (ν₀) of the material. Point D corresponds to a frequency less than the threshold frequency. Hence, there is no photoelectric emission for the λ5 line, and therefore, no stopping voltage is required to stop the current.