The quantum number of four electrons (el to e4) are given below :- `{:(,n,,l,,m,,s,,),(e1,3,,0,,0,,+1//2,,),(e2,4,,0,,0,,1//2,,),(e3,3,,2,,2,,-1//2,,),(e4,3,,1,,-1,,1//2,,):}` The correct order of decreasing energy of these electrons is :
A
`e4 gt e3 gt e2 gt e1`
B
`e2 gt e3 gt e4 gt e1`
C
`e3 gt e2 gt e4 gt e1`
D
`e1 gt e4 gt e2 gt e3`
Text Solution
AI Generated Solution
The correct Answer is:
To determine the correct order of decreasing energy of the electrons based on their quantum numbers, we will follow these steps:
### Step 1: Identify the Quantum Numbers
The quantum numbers for the electrons are:
- \( e_1: (n=3, l=0, m=0, s=+\frac{1}{2}) \)
- \( e_2: (n=4, l=0, m=0, s=+\frac{1}{2}) \)
- \( e_3: (n=3, l=2, m=2, s=-\frac{1}{2}) \)
- \( e_4: (n=3, l=1, m=-1, s=+\frac{1}{2}) \)
### Step 2: Calculate \( n + l \) Values
Next, we calculate the \( n + l \) values for each electron:
- For \( e_1 \): \( n + l = 3 + 0 = 3 \)
- For \( e_2 \): \( n + l = 4 + 0 = 4 \)
- For \( e_3 \): \( n + l = 3 + 2 = 5 \)
- For \( e_4 \): \( n + l = 3 + 1 = 4 \)
### Step 3: Determine Energy Order Based on \( n + l \)
The energy of an electron in an orbital is determined primarily by the \( n + l \) value:
- Higher \( n + l \) value means higher energy.
- If two orbitals have the same \( n + l \) value, the one with the higher \( n \) value has higher energy.
### Step 4: List \( n + l \) Values
Now we can list the \( n + l \) values:
- \( e_1: 3 \)
- \( e_2: 4 \)
- \( e_3: 5 \)
- \( e_4: 4 \)
### Step 5: Order by Energy
1. **Highest Energy**: \( e_3 \) (5)
2. **Next Highest**: \( e_2 \) (4) and \( e_4 \) (4) - compare \( n \) values:
- \( e_2 \) has \( n = 4 \) (higher)
- \( e_4 \) has \( n = 3 \) (lower)
3. **Lowest Energy**: \( e_1 \) (3)
### Final Order of Decreasing Energy
Thus, the order of decreasing energy is:
1. \( e_3 \)
2. \( e_2 \)
3. \( e_4 \)
4. \( e_1 \)
### Conclusion
The correct order of decreasing energy for the electrons is:
**\( e_3, e_2, e_4, e_1 \)**
---
NARENDRA AWASTHI ENGLISH|Exercise Match the column|1 Videos
Similar Questions
Explore conceptually related problems
The quantum number of four electrons (el to e4) are given below :- {:(,n,,l,,m,,s,,),(e1,3,,0,,0,,+1//2,,),(e2,4,,0,,1,,1//2,,),(e3,3,,2,,2,,-1//2,,),(e4,3,,1,,-1,,1//2,,):} The correct order of decreasing energy of these electrons is :
The quantum numbers for the outer electrons of an atom are given by n = 2, l = 0, m = 0, s = +1//2
The quantum number of four electrons are given below: n=4,l=2,m_(l)=-2,m_(s)=-1//2 n=3,l=2,m_(l),m_(s)=+1//2 n=4,l=1,m_(l)=0,m_(s)=+1//2 n=3,l=1,m_(l)=1,m_(s)=-1//2 The correct order of their increasing energies will be:
The quantum number of four electrons are given below: I. n=4,l=2,m_l=-2,m_s=-1/2 II. n=3,l=2,m_l=1,m_s=+1/2 III. n = 4 , l =1 ,m _l=0 ,m_s=+1/2 IV. n=3,l=1,m_l=1,m_s=-1/2 The correct order of their increasing energies will be
Which of the following sets of quantum numbers represent an impossible arrangement :- {:(,n,l,m,m_(s),),((A),3,2,-2,(1)/(2),),((B),4,0,0,(1)/(2),),((C),3,2,-3,(1)/(2),),((D),5,3,0,(1)/(2),):}
Consider the following sets of quantum numbers. (i) {:(n,l,m,s,),(3,0,0,+1//2,):} (ii) {:(n,l,m,s,),(2,2,1,+1//2,):} (iii) {:(n,l,m,s,),(4,3,-2,-1//2,):} (iv) {:(n,l,m,s,),(1,0,-1,-1//2,):} (v) {:(n,l,m,s,),(3,2,3,+1//2,):} Which of the following sets of quantum number is not possible ?
Which of the following sets of quantum numbers are impossible for electrons? Explain why in each case. |{:("Set",n,l,m,s),((i),1,0,1,+1/2),((ii),3,0,0,-1/2),((iii),1,2,2,+1/2),((iv),4,3,-3,+1/2),((v),5,2,1,-1/2),((vi),3,2,1,0):}|
The number of real roots of the equation x^5+e^(8x)=0 is (1)0 (2) 1 (3) 2 (4) 3
Let E=(1,2,3,4) and F-(1,2) . Then the number of onto functions from E to F is:
Find number of real roots of equation e^(4x) + e^(3x) - 4e^(2x) + e^(x) + 1 = 0 is
