If the atom follows the Bohr model and the radius of is times the Bohr radius, then find . [2003]

Question

If the atom ${}_{100}{Fm}^{257}$ follows the Bohr model and the radius of ${}_{100}{Fm}^{257}$ is $n$ times the Bohr radius, then find $n$ . [2003]

Smart Achievers · Accepted Answer

(4)

For an atom following Bohr's model, the radius of the fifth orbit.

$r_{m} = \frac{r_{0} m^{2}}{Z},$ where $r_{0}$ = Bohr's radius.

For ${}_{100}{Fm}^{257}$ , $m = 5$ (Fifth orbit in which the outermost electron is present) and $Z = 100$

$∴$ $r_{m} = \frac{r_{0} \times 5^{2}}{100} = n r_{0}$ $(given)$

$∴$ $n = \frac{1}{4}$

Solution

Q.
If the atom ${}_{100}{Fm}^{257}$ follows the Bohr model and the radius of ${}_{100}{Fm}^{257}$ is $n$ times the Bohr radius, then find $n$ . [2003]

1 $100$

2 $200$

3 $4$

4 $\frac{1}{4}$

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Solution

Q. If the atom Fm100257 follows the Bohr model and the radius of Fm100257 is n times the Bohr radius, then find n. [2003]

1 100

2 200

3 4

4 14