2.52 Following results are observed when sodium metal is irradiated with different wavelengths. Calculate (a) threshold wavelength and, (b) Planck’s constant.
λ (nm) | 500 | 450 | 400 |
v × 10–5 (cm s–1) | 2.55 | 4.35 | 5.35 |
(a) Assuming the threshold wavelength to be λ0 nm(=λ0 x 10-9 m), the kinetic energy of the radiation is given as:
h(v - v0) = 12 mv2
Three different equalities can be formed by the given value as:
hc(1λ - 1λ0) = 12 mv2
hc(1500 x 109 - 1λ0 x 10-9 m) = 12 m(2.55 x 10+5 x 10-2 m/s)
hc10-9m[1500 - 1λ0] = 12m(2.55 x 10+3 m/s)2 (1)
Similarly,
hc10-9m[1450 - 1λ0] = 12m(3.45 x 10+3 m/s)2 (2)
hc10-9m[1400 - 1λ0] = 12m(5.35 x 10+3 m/s)2 (3)
Dividing equation (3) by equation (1):
[1400 - 1λ0][1500 - 1λ0] = (5.35 x 10+3 m/s)2(2.55 x 10+3 m/s)2
5λ0 - 20004λ0 - 2000 = (5.352.55)2 = 28.62256.5025
5λ0 - 20004λ0 - 2000 = 4.40177
17.6070λ0 - 5λ0 = 8803.537 - 2000
λ0 = 6805.53712.607
λ0 = 539.8 nm
λ0 = 540 nm
So, threshold wavelength (λ0) = 540 nm
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