Which of the following sets of quantum numbers are allowed for an electron in a hydrogen atom?

a)n=3, l=0, ml=0
b)n=4,l=1,ml=-1
c)n=2,l=1,ml=-2

a. n can be 3 for an excited H atom; l can be 2,1,0; ml can be 0. OK for a.

b. n can be 4 for an excited H atom; l can be 3,2,1,0; ml can be -1,0,+1. OK for b.

c. n can be 2 for an excited H atom. l can be 1,0. mL can be -1,0,+1 but not -2. not OK. c is out.

To determine which sets of quantum numbers are allowed for an electron in a hydrogen atom, we need to consider the rules and restrictions for quantum numbers:

1. The principal quantum number (n) represents the energy level or shell of an electron. It must be a positive integer (1, 2, 3, etc.). All three given options satisfy this condition.

2. The azimuthal quantum number (l) represents the orbital angular momentum and depends on the value of n. It can range from 0 to (n-1) for a given value of n. So, for each option, we need to check if l is within the allowed range.

3. The magnetic quantum number (ml) represents the orientation of the orbital within a given subshell. Its values range from -l to +l. Therefore, we need to check if the value of ml in each option is within the range defined by the value of l.

Now let's go through each option:

a) Set a: n=3, l=0, ml=0
With n = 3, l can range from 0 to (3-1) = 2. Since l = 0, it satisfies this condition. Additionally, for l = 0, ml always equals zero. Therefore, this set of quantum numbers is allowed.

b) Set b: n=4, l=1, ml=-1
With n = 4, l can range from 0 to (4-1) = 3. Since l = 1, it satisfies this condition. The magnetic quantum number, ml, can range from -l to +l. For l = 1, ml can be -1, 0, or +1. Since ml = -1 in this option, it satisfies this condition. Therefore, this set of quantum numbers is allowed.

c) Set c: n=2, l=1, ml=-2
With n = 2, l can range from 0 to (2-1) = 1. Since l = 1, it satisfies this condition. The magnetic quantum number, ml, can range from -l to +l. For l = 1, ml can be -1, 0, or +1. Since ml = -2 in this option, it does not satisfy this condition. Therefore, this set of quantum numbers is not allowed.

In summary, the allowed sets of quantum numbers for an electron in a hydrogen atom out of the given options are:
a) n=3, l=0, ml=0
b) n=4, l=1, ml=-1

To determine which sets of quantum numbers are allowed for an electron in a hydrogen atom, we need to consider the limitations imposed by the quantum mechanical principles. These principles include the principal quantum number (n), the azimuthal quantum number (l), and the magnetic quantum number (ml).

The principal quantum number (n) represents the energy level or shell in which the electron is located. It can have any positive integer value starting from 1. Therefore, option a) with n = 3 is allowed.

The azimuthal quantum number (l) represents the orbital shape and ranges from 0 to (n-1). It determines the subshells within an energy level, with l = 0 representing an s orbital, l = 1 representing a p orbital, l = 2 representing a d orbital, and so on. Therefore, option a) with l = 0 and option c) with l = 1 are allowed. However, option b) with l = 1 is incorrect; it is outside the allowed range for the given value of n (n=4).

The magnetic quantum number (ml) represents the orbital orientation and can have values ranging from -l to +l. It determines the specific orbital within a subshell. For example, for an l = 1 (p orbital), ml can be -1, 0, or 1. Therefore, option a) with ml = 0 is allowed. Option b) with ml = -1 is allowed if it had a correct value for l. Option c) with ml = -2 is incorrect; it is outside the allowed range for the given value of l.

In summary, the correct answer is:
a) n=3, l=0, ml=0.

Which of the following sets of quantum numbers IS ALLOWED