Question

In an element with atomic number (Z) 25, the number of electrons with (n + l) value equal to 3 and 4 are x and y respectively. The value of (x + y) is

• A. 21
• B. 12
• C. 14
• D. 16

Hint:

The (n + l) rule helps determine the order of filling subshells in an atom; electrons with specific (n + l) values can be counted by examining the electron configuration.

Answer 1

The Correct Option is D

Let’s break this down step by step to calculate the number of electrons with specific (n + l) values and determine why option (4) is the correct answer.
Step 1: Understand the electron configuration of the element
The atomic number $Z = 25$ corresponds to manganese (Mn). Its electron configuration is:
\[ \text{Mn: } 1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 3d^5 \, 4s^2 \]
Total electrons = 25, which matches the atomic number.
Step 2: Calculate the (n + l) values for each subshell

• For $1s^2$: $n = 1$, $l = 0$, $n + l = 1$, 2 electrons.
• For $2s^2$: $n = 2$, $l = 0$, $n + l = 2$, 2 electrons.
• For $2p^6$: $n = 2$, $l = 1$, $n + l = 3$, 6 electrons.
• For $3s^2$: $n = 3$, $l = 0$, $n + l = 3$, 2 electrons.
• For $3p^6$: $n = 3$, $l = 1$, $n + l = 4$, 6 electrons.
• For $3d^5$: $n = 3$, $l = 2$, $n + l = 5$, 5 electrons.
• For $4s^2$: $n = 4$, $l = 0$, $n + l = 4$, 2 electrons.

Step 3: Sum the electrons with (n + l) = 3 and (n + l) = 4

• For $n + l = 3$:
  • $2p^6$: 6 electrons
  • $3s^2$: 2 electrons
  Total = $6 + 2 = 8$ (so $x = 8$).
• For $n + l = 4$:
  • $3p^6$: 6 electrons
  • $4s^2$: 2 electrons
  Total = $6 + 2 = 8$ (so $y = 8$).

\[ x + y = 8 + 8 = 16 \]
Step 4: Confirm the correct answer
The value of $x + y$ is 16, which matches option (4).
Thus, the correct answer is (4) 16.