Question

If the radius of the $3^{\text {rd }}$ Bohr's orbit of hydrogen atom is $r_{3}$ and the radius of $4^{\text {th }}$ Bohr's orbit is $r_{4}$. Then :

• A. $r _{4}=\frac{9}{16} r _{3}$
• B. $r_{4}=\frac{16}{9} r_{3}$
• C. $r_{4}=\frac{3}{4} r_{3}$
• D. $r_{4}=\frac{4}{3} r_{3}$

Answer 1

Answer: (B)

$r =0.529 \times \frac{ n ^{2}}{ z } \,\mathring{A}$
$r _{3}=0.529 \times \frac{3^{2}}{1}$
$r _{4}=0.529 \times \frac{4^{2}}{1}$
$\frac{ r _{4}}{ r _{3}}=\frac{4^{2}}{3^{2}}=\frac{16}{9}$
$r _{4}=\frac{16 r _{3}}{9}$