Q27 of 43 Page 409

Monochromatic radiation of wavelength 640.2 nm (1nm = 10–9 m) from a neon lamp irradiates photosensitive material made of caesium on tungsten. The stopping voltage is measured to be 0.54 V. The source is replaced by an iron source and its 427.2 nm line irradiates the same photo-cell. Predict the new stopping voltage.

Given:


Wavelength of light, λ = 640.2 nm = 640.2 × 10-9m


Stopping potential, V0 = 0.54 V


Let frequency of light = v


Work function, Φ0 is given by,


Φ0 = hv-eVs


Φ0 = …(1)


Where,


h = Planck’s constant = 6.6 × 10-34Js


c = speed of light = 3 × 108m


λ = wavelength of light


e = charge on each electron = 1.6 × 10-19C


Φ0 =


Φ0 = 2.229 × 10-19J or 1.39 eV


Wavelength of radiation emitted by iron, λ’ = 427.2 nm


λ’ = 4.27.2 × 10-9m


The new stopping potential can be found using equation (1),


Let new stopping potential = v’


By putting the values in equation (1) we get,


Φ0 =


→


→


→ v’ = 1.5 eV


Therefore, the new stopping potential is 1.5 eV.


More from this chapter

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25

Estimating the following two numbers should be interesting. The first number will tell you why radio engineers do not need to worry much about photons! The second number tells you why our eye can never ‘count photons’, even in the barely detectable light.

(a) The number of photons emitted per second by a Medium wave transmitter of 10 kW power, emitting radio waves of wavelength 500 m.


(b) The number of photons entering the pupil of our eye per second corresponding to the minimum intensity of white light that we humans can perceive (∼10–10 W m–2). Take the area of the pupil to be about 0.4 cm2, and the average frequency of white light to be about 6 × 1014 Hz.

 26

Ultraviolet light of wavelength 2271 Å from a 100 W mercury source irradiates a photo-cell made of molybdenum metal. If the stopping potential is –1.3 V, estimate the work function of the metal. How would the photo-cell respond to a high intensity (∼105 W m–2) red light of wavelength 6328 Å produced by a He-Ne laser?

 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:

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.]

 29

The work function for the following metals is given:

Na: 2.75 eV; K: 2.30 eV; Mo: 4.17 eV; Ni: 5.15 eV. Which of these metals will not give photoelectric emission for a radiation of wavelength 3300 Å from a He-Cd laser placed 1 m away from the photocell? What happens if the laser is brought nearer and placed 50 cm away?