Following results are observed when sodium metal is irradiated with different wavelengths. Calculate (a) threshold wavelength and, (b) Planck’s constant



Q.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

Answer:-
Let the threshold wavelength to be λnm = λ0×10-9 m . 
Following equation holds true for photoelectric emission in given case:
K.E. = 1/2 mv= h(ν  ν0)
⇒1/2 mv= hν  0
⇒ hν= hν – 1/2 mv2
⇒ hc/λ0 = hc/λ – 1/2 mv2



(a) Substituting the value of λ and v from the above given data, we get three values of λas,
λ0(1) = 541 nm
λ0(2) = 546 nm
λ0(3) = 542 nm
Threshold frequency = λav = {λ0(1)0(2)0(3)}/3 = (541+546+542)/3 = 543 (approx 540)
(b) Part of this question can’t be solved due to incorrect value of v i.e 5.35.
Students can assume this value as 5.20 if they want to solve this question.