Chapter 36: Problem 4

Both the Bohr and Schrödinger theories predict the same groundstate energy for hydrogen. Do they agree about the angular momentum in the ground state? Explain.

Short Answer

Expert verified

No, the Bohr and Schrödinger theories do not agree on the predicted angular momentum of hydrogen in its ground state. According to Bohr, the angular momentum is \( \hbar \), while, as per Schrödinger, it is \( 0 \).

Step by step solution

Explain Bohr model's prediction

According to Bohr's model, electrons move in defined circular orbits. The angular momentum \(L\) is quantized, which means it can only take up certain unique values, and for the ground state (n=1), it is given by \(L = n \hbar\) where \(\hbar\) is the reduced Planck's constant and \(n\) is the principal quantum number. Thus, for the ground state, \(L = \hbar\).

Explain Schrödinger model's prediction

In Schrödinger's quantum mechanical model, the angular momentum is also quantized, but the ground state of the hydrogen atom corresponds to zero orbital angular momentum. Here, ground state refers to the lowest energy state (n=1) with the lowest angular momentum quantum number (\(l=0\)). So, for a hydrogen atom in its ground state according to Schrödinger's model, the angular momentum \(L = 0\).

Conclusion

From the predictions of angular momentum from both theories, it can be seen that the Bohr model and the Schrödinger model do not agree about the angular momentum of hydrogen atom in its ground state.

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Both the Bohr and Schrödinger theories predict the same groundstate energy for hydrogen. Do they agree about the angular momentum in the ground state? Explain.

Short Answer

Step by step solution

Explain Bohr model's prediction

Explain Schrödinger model's prediction

Conclusion

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