In Bohr theory of hydrogen atom, let r, v and E be the radius of orbit, speed of electron and the total energy of the electron respectively. Which of the following quantities is proportional to the quantum number n?

Question

In Bohr theory of hydrogen atom, let r, v and E be the radius of orbit, speed of electron and the total energy of the electron respectively. Which of the following quantities is proportional to the quantum number n? (A) vr (B) rE (C) (r/E ) (D) (r/ upsilon )

Tardigrade Admin · Accepted Answer

According to Bohr theory of hydrogen atom r â n2 upsilon â (1/n) E propto (1/n2) ∴ upsilon r â n

Q. In Bohr theory of hydrogen atom, let r, v and E be the radius of orbit, speed of electron and the total energy of the electron respectively. Which of the following quantities is proportional to the quantum number n?

$v r$

$r E$

$\frac{r}{E}$

$\frac{r}{υ}$

According to Bohr theory of hydrogen atom
$r \propto n_{2}$
$υ \propto \frac{1}{n}$
$E \propto \frac{1}{n ^{2}} ∴ υ r \propto n$