Question

The energy of the second Bohr orbit of the hydrogen atom is -328 kJ mol^-1; hence the energy of the fourth Bohr orbit would be:

• A. - 41 kJ mol^-1
• B. -1224 kJ mol^-1
• C. -284 kJ mol^-1
• D. -82 kJ mol^-1

Answer 1

The Correct Option is D

To solve the problem of finding the energy of the fourth Bohr orbit given the energy of the second Bohr orbit, we will use the formula for the energy of an electron in the nth orbit for a hydrogen atom:

E_n = -\frac{13.6 \, \text{kJ}}{n^2} \times Z^2

where E_n is the energy of the electron, n is the orbit number, and Z is the atomic number of the hydrogen atom, which is 1.

Given:

• The energy of the second Bohr orbit (n=2) is -328 kJ/mol.

First, we calculate the energy of the second Bohr orbit using the formula:

E_2 = -\frac{13.6}{2^2} \, \text{kJ} \cdot 1^2 = -\frac{13.6}{4} \, \text{kJ} = -3.4 \, \text{kJ/electron}

Since it is given that E_2 is -328 kJ/mol, this matches the value calculated for -3.4 kJ/electron when multiplied by Avogadro's number (approximately 6.022 \times 10^{23}), confirming the problem statement.

Next, we determine the energy of the fourth Bohr orbit, (n=4):

E_4 = -\frac{13.6}{4^2} \, \text{kJ} = -\frac{13.6}{16} \, \text{kJ} = -0.85 \, \text{kJ/electron}

Calculating this for one mole of electrons by multiplying by Avogadro's number gives us:

E_4 = -0.85 \times 6.022 \times 10^{23} \approx -82 \, \text{kJ/mol}

Thus, the energy of the fourth Bohr orbit is -82 kJ/mol.

The correct answer is therefore -82 kJ/mol, as this matches our calculation based on the Bohr energy formula.