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Chapter 6: Problem 100

What is the radius of a hydrogen atom when the electron is in the first excited state?

Short Answer

Expert verified
The radius of a hydrogen atom when the electron is in the first excited state (n=2) is approximately \(2.116 Å\).

Step by step solution

01

Calculate the radius of the orbit in the first excited state

To calculate the radius of the orbit in the first excited state, we need to plug the value of n=2 for the second energy level, along with the value of the Bohr radius, into the formula above. Using the given formula, we have: \[r_2 = a_0 (2)^2\]
02

Compute the numerical value of the radius

Now, we need to substitute the value of the Bohr radius (\(a_0\)), which is approximately 0.529 Å, into our expression: \[r_2 = (0.529 Å)(2)^2\] By solving this expression, we obtain the radius of the hydrogen atom when the electron is in the first excited state: \[r_2 = (0.529 Å)(4)\] \[r_2 = 2.116 Å\] So, the radius of a hydrogen atom when the electron is in the first excited state is approximately 2.116 Å.

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Most popular questions from this chapter

What is the longest wavelength that light can have if it is to be capable of ionizing the hydrogen atom in its ground state?

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