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: Eliminate wrong signs
Energy of a bound electron must be negative, so $+2.18\times 10^{-18}\ \text{J}$ is wrong.

Step 2: Check the magnitude
The value $52.9\ \text{J}$ mixes up with the Bohr radius (52.9 pm), and $-1.09\times 10^{-18}\ \text{J}$ is half of the correct value.

Step 3: Conclusion
The correct value is $-2.18\times 10^{-18}\ \text{J}$.

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