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Dual Nature of Radiation and Matter

  1. The photoelectric threshold wavelength of silver is 3250 × 10–10 m. The velocity of the electron ejected from a silver surface by ultraviolet light of wavelength 2536 × 10–10 m is
    (Given h = 4.14 × 10–15 eVs and c = 3 × 108 ms–1)
    1. ≈0.6 × 106 ms–1
    2. ≈61 × 103 ms–1
    3. ≈0.3 × 106 ms–1
    4. ≈6 × 105 ms–1
    5. A and D Both
Correct Option: E

Both answers are correct ​Given,
λ0 = 3250 × 10–10 m
λ = 2536 × 10–10 m ​

φ =
hc
=
4.14 × 10-15 × 3 × 108
= 3.82eV
λ0 3250 × 10-10

hv =
hc
=
4.14 × 10-15 × 3 × 108
= 4.89eV
λ2536 × 10-10

According to Einstein's photoelectric equation, ​
Kmax = hv – φ
KEmax = (4.89–3.82)eV=1.077 eV
1
= 1.077 × 1.6 × 10–19
2

⇒ v =
2 × 1.077 × 1.6 × 10-19
9.1 × 10-31

or,  v = 0.6 × 106 m/s or 6 × 105 m/s



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