Question

Calculate the energy associated with an electron in the first orbit of hydrogen atom?

• A. \(-2.18\times 10^{-18}\ \text{J}\)
• B. \(52.9\ \text{J}\)
• C. \(-1.09\times 10^{-18}\ \text{J}\)
• D. \(2.18\times 10^{-18}\ \text{J}\)

Hint:

Use the Bohr energy formula with n = 1 and Z = 1.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
The Bohr energy of an electron in the nth orbit is \(E_{n} = -2.18\times 10^{-18}\,\dfrac{Z^{2}}{n^{2}}\ \text{J}\).

Step 2: Calculation
For hydrogen \(Z = 1\), and for the first orbit \(n = 1\).
\(E_{1} = -2.18\times 10^{-18}\ \text{J}\).

Step 3: Meaning of the sign
The negative sign shows the electron is bound to the nucleus. In electron volts this is \(-13.6\ \text{eV}\).

Final Answer:
The energy of the electron in the first orbit is minus 2.18 times 10 to the power minus 18 joule. \[ \boxed{\text{(A) }-2.18\times 10^{-18}\ \text{J}} \]