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.]

Asked by Nagasanthoshi 14/10/2019 Last Modified 23/10/2019

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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.]

Asked by Nagasanthoshi 14/10/2019 Last Modified 23/10/2019

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Harshit Bhardwaj · Accepted Answer

Einstein’s photoelectric equation is given as:

eV₀ = hν−

Where,

V₀ = Stopping potential

h = Planck’s constant

e = Charge on an electron

ν = Frequency of radiation

= Work function of a material

It can be concluded from equation (1) that potential V₀ is directly proportional to frequency ν.

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:

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 νand 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.

Slope of the straight line =

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

The work function of the metal is given as:

= hν₀

= 6.573 × 10⁻³⁴ × 5 × 10¹⁴

= 3.286 × 10⁻¹⁹ J

= 2.054 eV

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