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.

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. (A) 100 (B) 200 (C) 4 (D) (1/4)

Tardigrade Admin · Accepted Answer

According to Bohr's model, rm=((m2/Z)) × r0 where m= orbit number, r0= Bohr radius For 100 Fm 257, Z=100 ∴ m=5 ∴ rm=((5)2/100) r0 According to given problem n r0=((5)2/100) r0 or n=(1/4)

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

100

200

4

$\frac{1}{4}$

According to Bohr's model, $r_{m} = (\frac{m ^{2}}{Z}) \times r_{0}$
where $m =$ orbit number, $r_{0} =$ Bohr radius
For $_{100} F m^{257}, Z = 100$
$∴ m = 5$
$∴ r_{m} = \frac{( 5 ) ^{2}}{100} r_{0}$
According to given problem
$n r_{0} = \frac{( 5 ) ^{2}}{100} r_{0}$ or $n = \frac{1}{4}$

Q. If the atom 100​Fm257 follows the Bohr model and the radius of 100​Fm257 is n times the Bohr radius, then find n.

100

200

4

41​

According to Bohr's model, rm​=(Zm2​)×r0​ where m= orbit number, r0​= Bohr radius For 100​Fm257,Z=100 ∴m=5 ∴rm​=100(5)2​r0​ According to given problem nr0​=100(5)2​r0​ or n=41​

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

$\frac{1}{4}$

According to Bohr's model, $r_{m} = (\frac{m ^{2}}{Z}) \times r_{0}$
where $m =$ orbit number, $r_{0} =$ Bohr radius
For $_{100} F m^{257}, Z = 100$
$∴ m = 5$
$∴ r_{m} = \frac{( 5 ) ^{2}}{100} r_{0}$
According to given problem
$n r_{0} = \frac{( 5 ) ^{2}}{100} r_{0}$ or $n = \frac{1}{4}$