NEET 2025 — Chemistry solution

NEET2025Chemistry

Energy and radius of first Bohr orbit of He $^{+}$ and Li $^{2 +}$ are

[Given $R_{H} = 2.18 \times 1 0^{- 18}$ J, $a_{0} = 52.9$ pm]

A
$E_{n} (Li^{2 +}) = - 19.62 \times 1 0^{- 18}$ J; $r_{1} (Li^{2 +}) = 17.6$ pm; $E_{n} (He^{+}) = - 8.72 \times 1 0^{- 18}$ J; $r_{1} (He^{+}) = 26.4$ pm
B
$E_{n} (Li^{2 +}) = - 8.72 \times 1 0^{- 18}$ J; $r_{1} (Li^{2 +}) = 26.4$ pm; $E_{n} (He^{+}) = - 19.62 \times 1 0^{- 18}$ J; $r_{1} (He^{+}) = 17.6$ pm
C
$E_{n} (Li^{2 +}) = - 19.62 \times 1 0^{- 16}$ J; $r_{1} (Li^{2 +}) = 17.6$ pm; $E_{n} (He^{+}) = - 8.72 \times 1 0^{- 16}$ J; $r_{1} (He^{+}) = 26.4$ pm
D
$E_{n} (Li^{2 +}) = - 8.72 \times 1 0^{- 16}$ J; $r_{1} (Li^{2 +}) = 17.6$ pm; $E_{n} (He^{+}) = - 19.62 \times 1 0^{- 16}$ J; $r_{1} (He^{+}) = 17.6$ pm

Solution

$E_{n} = - 2.18 \times 1 0^{- 18} \cdot \frac{Z ^{2}}{n ^{2}}$ J. For first orbit ( $n = 1$ ):

He $^{+}$ ( $Z = 2$ ): $E_{1} = - 2.18 \times 1 0^{- 18} \times 4 = - 8.72 \times 1 0^{- 18}$ J.

Li $^{2 +}$ ( $Z = 3$ ): $E_{1} = - 2.18 \times 1 0^{- 18} \times 9 = - 19.62 \times 1 0^{- 18}$ J.

Radius $r_{n} = 52.9 \cdot n^{2} / Z$ pm. For $n = 1$ :

He $^{+}$ : $r_{1} = 52.9/2 = 26.4$ pm.

Li $^{2 +}$ : $r_{1} = 52.9/3 = 17.6$ pm.

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