Let An be the area enclosed by the nth orbit in a hydrogen atom. The graph of In (An/A1) against In (n)

Q. Let A_n be the area enclosed by the nth orbit in a hydrogen atom. The graph of ln (A_n/A₁) against In (n)

(a) will not pass through origin

(b) will be a straight line with slope 4

(c) will be a rectangular hyperbola

(d) will be a parabola

Ans: (b)

Sol: A_n = π r_n²

A_n = π(r₀n²)²

Hence , A_n = πr₀²n⁴ = A₁r⁴

A_n/A₁ = n⁴

Taking log ,

ln(A_n/A₁) = 4ln(n)

Hence Straight line with slope 4 .