An electron in an atom is in a state with The minimum angle between and the z axis is:
A) 0$\degree$
B) 18.0$\degree$
C) 24.1$\degree$
D) 36.7$\degree$
E) 33.6$\degree$

Question

An electron in an atom is in a state with  The minimum angle between  and the z axis is:
A) 0$\degree$ 
B) 18.0$\degree$ 
C) 24.1$\degree$ 
D) 36.7$\degree$ 
E) 33.6$\degree$

Quizplus · Accepted Answer

The state with 11eaafba_aef5_22f4_a7a5_1f16b7642120_TB3976_11 gives us the values of n (11) and l (2). The minimum angle between the z axis and the vector representing this state, which is given by 11eaafba_aef5_4a05_a7a5_3d50c32a5931_TB3976_11, can be calculated using the formula:

cos(theta) = m_l / (l(l+1))^0.5

where m_l is the magnetic quantum number and l is the azimuthal quantum number. For this state, m_l can take the values -2, -1, 0, 1, or 2 since l = 2. Plugging these values into the formula and taking the absolute value, we get:

|cos(theta)| = 2 / 6^0.5 = 0.8165

Therefore, the minimum angle between the vector and the z axis is:

theta = acos(0.8165) = 24.1 degrees

so the correct answer is choice C.

An Electron in an Atom Is in a State with °\degree°

An Electron in an Atom Is in a State with $\degree$