NEETPhysicsAtomic Physics
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): The radius of the second stationary orbit of the Be ³⁺ ion is equal to the Bohr radius of the hydrogen atom. Reason (R): The radius of the n^ th Bohr orbit is directly proportional to n and inversely proportional to Z . In the light of the above statements, choose the correct answer from the option
Options
- ABoth (A) and (R) are true and (R) is the correct explanation of (A)
- BBoth (A) and (R) are true but (R) is not the correct explanation of (A)
- C(A) is true but (R) is false
- D(A) is false but (R) is true
Correct answer
C. (A) is true but (R) is false
Step-by-step solution
The radius of the n^ th Bohr orbit of a hydrogen-like species is given by: r_n = a₀ n^2 Z where a₀ is the Bohr radius of the hydrogen atom ( n=1, Z=1 ). For the Be ³⁺ ion, Z = 4 . The radius of its second stationary orbit ( n = 2 ) is: r = a₀ 2^2 4 = a₀ 4 4 = a₀ Thus, the radius of the second orbit of Be ³⁺ is exactly equal to the Bohr radius of the hydrogen atom. Therefore, Assertion (A) is true. The formula shows that the radius is directly proportional to the square of the principal quantum number ( n^2 ) and in