# Physics Class 12 NCERT Solutions: Chapter 11 Dual Nature of Radiation and Matter Part 13 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Q: 28. 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:

The stopping voltages, respectively, were measured to be:

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 ) . Experiments of this kind on , 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 .]

Einstein՚s photoelectric equation is given as:

Where,

Stopping potential

Planck՚s constant

Charge on an electron

Work function of a material

It can be concluded from equation (1) that potential is directly proportional to frequency .

Frequency is also given by the relation:

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:

The following figure shows a graph between v and .

It can be observed that the obtained curve is a straight line. It intersects the , which is the threshold frequency of the material. Point D corresponds to a frequency less than the threshold frequency. Hence, there is no photoelectric emission for the line, and therefore, no stopping voltage is required to stop the current. Slope of the straight line

From equation (1) , the slope can be written as:

The work function of the metal is given as: