Question

The energy associated with the first Orbit in a hydrogen atom is -2.18 × 10^-18 J. What is the energy associated with the 5th Orbit?

A) -5.45 × 10^-19 J
B) -2.18 × 10^-17 J
C) -2.44 × 10^-20 J
D) -8.72 × 10^-18 J

Answer 1

The energy associated with the 5th orbit in a hydrogen atom is calculated using the Bohr model and is found to be -8.72 × 10⁻²⁰ J, corresponding to option D).

Step-by-step explanation:

The energy associated with the first orbit in a hydrogen atom is given as -2.18 × 10⁻¹⁸ J. The energy of an electron in any orbit can be calculated using the equation derived from the Bohr model, which states that the energy levels of hydrogen are quantized and inversely proportional to the square of the quantum number n associated with each orbit. Mathematically, it is represented as
`E_n = E_1/n^2`, where
`E_1` is the energy of the first orbit and n is the principal quantum number of the orbit in question.

For the 5th orbit (n=5), we can calculate the energy as follows:

`E_5 = E_1/(5^2)`

= -2.18 × 10⁻¹⁸ J / 25

= -0.872 × 10⁻¹⁸ J or -8.72 × 10⁻²⁰ J.

Therefore, the energy associated with the 5th orbit in a hydrogen atom is -8.72 × 10⁻²⁰ J, which corresponds to option D).