Question 45: Dual Nature of Matter and Radiation

Question

In a historical experiment to determine  Planck's constant, a metal surface was  irradiated with light of different  wavelengths. The emitted  photoelectron energies were measured  by applying a stopping potential. The  relevant data for the wavelength ($$\lambda $$) of  incident light and the corresponding  stopping potential (V0) are given  below:

$$\lambda \left( {\mu m} ight)$$
V0(Volt)

0.3
2.0

0.4
1.0

0.5
0.4

Given that c = 3 $$ 	imes $$ 108  ms-1 and  e = 1.6 $$ 	imes $$ 10-19 C, Planck's constant (in  units of J-s) found from such an  experiment is) :

Accepted Answer

$${{hc} \over \lambda } - \phi  = e{V_0}$$ ($$\phi$$ = work function)
$${{hc} \over {0.3 	imes {{10}^{ - 6}}}} - \phi  = 2e$$ .... (i)
$${{hc} \over {0.4 	imes {{10}^{ - 6}}}} - \phi  = 1e$$ .... (ii)
Subtracting Eq. (ii) from Eq. (i)
$$hc\left( {{1 \over {0.3}} - {1 \over {0.4}}} ight){10^6} = e$$
$$hc\left( {{{0.1} \over {0.12}} 	imes {{10}^6}} ight) = e$$
$$h = 0.64 	imes {10^{ - 33}}$$
$$ = 6.4 	imes {10^{ - 34}}$$ J-s

Answer

6.0 $$ 	imes $$ 10-34

Answer

6.6 $$ 	imes $$ 10-34

Answer

6.4 $$ 	imes $$ 10-34

Answer

6.8 $$ 	imes $$ 10-34

Dual Nature of Matter and Radiation

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