A photosensitive metallic surface has work function, h v_o, If photons of energy 2hv_o_, fall on this surface, the electrons come out with a maximum velocity of 4 x 10⁶ m/s. When the photon energy is increased to 5 hv,, then maximum velocity of photoelectrons will be

2 × 10⁶ m/s

2 × 10⁷ m/s

8 × 10⁵ m/s

8 × 10⁶ m/s

Solution

8 × 10⁶ m/s

The solution to our problem consists in Einstein's photoelectric equation.

Einstein's photoelectric equation can be written as

$\frac{1}{2} {mv}^{2} = hν - ϕ \frac{1}{2} m \times {(4 \times 10^{6})}^{2} = 2 {hν}_{o} - {hν}_{o} . . . (i) and \frac{1}{2} \times m \times v^{2} = 5 {hν}_{o} - {hν}_{o} . . . . . . (ii)$

Dividing equation (ii) by eq (i)

$\Rightarrow \frac{ν^{2}}{{(4 \times 10^{6})}^{2}} = \frac{4 {hν}_{o}}{{hν}_{o}} \Rightarrow ν^{2} = 4 \times 16 \times 10^{12} ∴ v^{2} = 64 \times 10^{12} ν = 8 \times 10^{6} m / s$

The efficiency of photoelectric effect is less than 1 o .ie, number of photons less than 1 % are capable of ejecting photoelectrons.

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For Daily Free Study Material Join wiredfaculty

Dual Nature Of Radiation And Matter

Some More Questions From Dual Nature of Radiation and Matter Chapter

The time by a photoelectron to come out after the photon strikes is approximately

An alpha nucleus of energy 1 /2 mv2 bombards a heavy nuclear target of charge Ze. Then the distance of closest approach for the alpha nucleus will be proportional to

If I0 is the intensity of the principal maximum in the single slit diffraction pattern, then what will be its intensity when the slit width is doubled?

The maximum number of possible interference maxima for slit-separation equal to twice the wavelength in Young’s double-slit experiment is

According to Einstein’s photoelectric equation, the plot of the kinetic energy of the emitted photo electrons from a metal Vs the frequency, of the incident radiation gives straight line whose slope

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NCERT Sample Papers

Entrance Exams Preparation

An alpha nucleus of energy 1 /2 mv² bombards a heavy nuclear target of charge Ze. Then the distance of closest approach for the alpha nucleus will be proportional to

If I₀ is the intensity of the principal maximum in the single slit diffraction pattern, then what will be its intensity when the slit width is doubled?