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 , λ2= 4047 , λ3= 4358 , λ4= 5461 , λ5= 6907 , 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’* 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’* photoelectric equation and at the same time gave an independent estimate of the value of h.]

Answer 1

Einstein’* photoelectric equation is given as:

Where,
V0 = Stopping potential
h = Planck’* 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 V0.

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.