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Q47P

Expert-verifiedFound in: Page 1217

Book edition
10th Edition

Author(s)
David Halliday

Pages
1328 pages

ISBN
9781118230718

**For what value of the principal quantum number n would the effective radius, as shown in a probability density dot plot for the hydrogen atom, be 1.00 mm? Assume that has its maximum value of n-1. (Hint:See Fig.39-24.)**

The value of principal quantum number is $4.3\times {10}^{3}$.

The given data is listed below as,

- Radius of hydrogen atom is $r=1.00\mathrm{mm}=1.00\times {10}^{-3}\hspace{0.33em}\mathrm{m}$

**The principal quantum number is used to describe the electron’s state and is the one four quantum number assigned to each electron in an atom.**

**The value of the principal quantum number is natural number.**

According to the fig. 39-24. the principal quantum number satisfies,

$\mathrm{r}={\mathrm{n}}^{2}\mathrm{a}$

Here, the Bohr radius is $a=5.29\times {10}^{-13}\hspace{0.33em}m$.

Solving the above equation will give the value of the principal quantum number is,

$n=\sqrt{\frac{r}{a}}$

Substitute $1.00\times {10}^{-3}\mathrm{m}$ for r in the above equation.

$\mathrm{n}=\sqrt{\frac{1.00\times {10}^{-3}\mathrm{m}}{5.29\times {10}^{-13}\mathrm{m}}}\phantom{\rule{0ex}{0ex}}=4.3\times {10}^{3}$

Hence, the value of principal quantum number is $4.3\times {10}^{3}$.

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