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Atoms and Nuclei question

2023 · 6 Apr · Shift 1 · Q62
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Atoms and Nuclei question

2023 · 6 Apr · Shift 1 · Q62

JEE MainPhysicsAtoms and NucleiNumerical+4 / −1
The radius of fifth orbit of the Li++\mathrm{Li}^{++}Li++ is ‾\underline{\hspace{2cm}}​×10−12 m\times 10^{-12} \mathrm{~m}×10−12 m. Take: radius of hydrogen atom =0.51 Ao= 0.51\,\mathop A\limits^o=0.51Ao​
Numerical answer
View written solutionFree

Correct answer: 425

  1. Use Bohr radius formula for hydrogen-like species

For a hydrogen-like ion,

rn=a0 n2Z r_n = a_0\,\frac{n^2}{Z}rn​=a0​Zn2​

where:

  • a0=0.51 A˚a_0 = 0.51\,\text{Å}a0​=0.51A˚
  • n=5n = 5n=5
  • For Li++\mathrm{Li}^{++}Li++, atomic number Z=3Z=3Z=3
  1. Substitute the values
r5=0.51×523 A˚r_5 = 0.51\times \frac{5^2}{3}\,\text{Å}r5​=0.51×352​A˚ r5=0.51×253 A˚r_5 = 0.51\times \frac{25}{3}\,\text{Å}r5​=0.51×325​A˚ r5=4.25 A˚r_5 = 4.25\,\text{Å}r5​=4.25A˚
  1. Convert Å to meter

Since

1 A˚=10−10 m1\,\text{Å} = 10^{-10}\,\text{m}1A˚=10−10m

we get

r5=4.25×10−10 mr_5 = 4.25\times 10^{-10}\,\text{m}r5​=4.25×10−10m
  1. Express in the required form

We need

r5=___×10−12 mr_5 = \boxed{\_\_\_}\times 10^{-12}\,\text{m}r5​=___​×10−12m

Now,

4.25×10−10=425×10−124.25\times 10^{-10} = 425\times 10^{-12}4.25×10−10=425×10−12

So the required integer is

425\boxed{425}425​
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