Verified Solution • 2025–26 Session moderate

QJEEM25Ch5c92: JEE Main 2025 Chemistry - Class 11 JEEM25Ch5c92 Solution: Radius of the first excited state of Helium ion is given as :…

Radius of the first excited state of Helium ion is given as : a0→\mathrm{a}_0 \rightarrow radius of first stationary state of hydrogen atom.

Multiple Choice Options

  • A r=a04\mathrm{r}=\frac{\mathrm{a}_0}{4}
  • B r=2a0\mathrm{r}=2 \mathrm{a}_0
  • C r=4a0\mathrm{r}=4 \mathrm{a}_0
  • D r=a02\mathrm{r=\frac{a_0}{2}}

Step-by-Step Verified Solution

rn=n2 a0Zr_n = \frac{n^2\, a_0}{Z}

For the helium ion, which is hydrogen-like with a nuclear charge of Z=2Z = 2 , the first excited state corresponds to n=2n = 2 . Substituting these values:

r2=(2)2 a02=4 a02=2 a0r_2 = \frac{(2)^2\, a_0}{2} = \frac{4\, a_0}{2} = 2\, a_0

Thus, the radius of the first excited state of the helium ion is 2 a02\, a_0 .

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