Question

Let $T_1$ and $T_2$ be the energy of an electron in the first and second excited states of the hydrogen atom, respectively. According to Bohr’s model of an atom; the ratio T1:T2 is:

• A. $1:4$
• B. $4:1$
• C. $4:9$
• D. $9:4$

Answer 1

Answer: (D)

$9:4$

Answer 2

The first statement can be rephrased as follows:

• The energy of an electron in an atom can be calculated using the formula
  $E_n = -13.6(\frac{z^2}{n^2})$,
  where $z$ is the atomic number and n is the principal quantum number.
  When $n=2$, the energy of the first excited state is $E_2$.

The second statement can be rephrased as follows:

• The ratio of the temperatures $T_1$ and $T_2$ is equal to the ratio of energies $E_2$ and $E_3$,
  which is $\frac{32}{22}$ or $\frac{9}{4}$.
  Therefore, the temperature of the second excited state $(n=3)$ is equal to $E_3$,
  while the temperature of the first excited state $(n=2)$ is denoted by $T_1$.