51.
In which state Be3+ will have same orbital radius as that of ground state of hydrogen atom ?
Exam Year(s)
MH SET - 2025, SET Exam - 2025,
Answer: C
Be3+ has the hydrogen ground-state radius in the state n = 2.
For a hydrogen-like ion the Bohr radius of orbit n is
\[ r_{n} = \frac{n^{2}a_{0}}{Z} \]
For hydrogen in its ground state, n = 1 and Z = 1, so r = a0. For Be3+, Z = 4, so \(r_{n} = a_{0}\) requires \(n^{2} = 4\), that is n = 2.
In n = 1 the Be3+ orbit is only a0/4, and n = 3 gives 9a0/4. n = 0 is not an allowed quantum number.
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