An orbital electron in the ground state of hydrogen has an angular momentum L1, and an orbital electron in the first orbit in the ground state of lithium atom has an angular momentum L2. a)L1 = L2b)L1 = 3L2 c)L2 = 3L1d)L2 = 9L1Correct answer is option 'A'. Can you explain this answer?

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Answer

Answer

Angular momentum = mω²r
as the radius increase the angular velocity decrease so the momentum is conserved and L1=L2

Answer

Angular Momentum in Quantum Mechanics

In quantum mechanics, the angular momentum of a particle is quantized, meaning it can only take on certain discrete values. The angular momentum is given by the formula L = √(l(l+1))ħ, where l is the quantum number associated with the angular momentum and ħ is the reduced Planck's constant.

Ground State of Hydrogen

The ground state of hydrogen is the state in which the electron is in the lowest energy level. In this state, the electron occupies the 1s orbital, which has a quantum number of l = 0. According to the formula for angular momentum, the angular momentum of the electron in the ground state of hydrogen is L1 = √(0(0+1))ħ = 0.

Ground State of Lithium

The ground state of lithium is the state in which the electrons are in their lowest energy levels. The first electron in lithium occupies the 1s orbital, which also has a quantum number of l = 0. Therefore, the angular momentum of this electron is also L2 = √(0(0+1))ħ = 0.

Comparison of Angular Momenta

From the calculations above, we can see that both L1 and L2 are equal to zero. Therefore, the correct answer is option A, L1 = L2. This means that the angular momentum of the electron in the ground state of hydrogen is equal to the angular momentum of the electron in the first orbit of the ground state of lithium.

Importance of Ground State

It is important to note that the given question specifies the ground state for both hydrogen and lithium. The ground state is the lowest energy state of an atom, and in this state, the electrons occupy the lowest energy levels. In the ground state, the electrons have the lowest possible energy and the lowest possible angular momentum. Therefore, it makes sense that both L1 and L2 are equal to zero in this case.

In conclusion, the angular momentum of the electron in the ground state of hydrogen (L1) is equal to the angular momentum of the electron in the first orbit of the ground state of lithium (L2). This is because both electrons are in their lowest energy levels, where the angular momentum is zero.

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