NEETChemistryStructure of Atom
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): The de-Broglie wavelength of an electron in the 3^ rd orbit of a Li ²⁺ ion is identical to the de-Broglie wavelength of an electron in the 1^ st orbit of a hydrogen atom. Reason (R): The de-Broglie wavelength of an electron in a Bohr orbit is directly proportional to the principal quantum number (
Options
- ABoth Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
- BAssertion (A) is true but Reason (R) is false.
- CAssertion (A) is false but Reason (R) is true.
- DBoth Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
Correct answer
D. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
Step-by-step solution
From Bohr's postulate, mvr = nh 2 . Using the de-Broglie relation = h mv , we get 2 r = n = 2 r n . The radius of a Bohr orbit is r = a₀ n^2 Z . Substituting r , the wavelength becomes = 2 a₀ n Z . This shows that n Z , making the Reason (R) true. For the 3^ rd orbit of Li ²⁺ ( n=3, Z=3 ), = 2 a₀ (3) 3 = 2 a₀ . For the 1^ st orbit of H atom ( n=1, Z=1 ), = 2 a₀ (1) 1 = 2 a₀ . Since both wavelengths are equal, the Assertion (A) is true. The Reason (R) provides the correct formula to explain the Assertion (A). Answer