Amongst the three isotopes of Neon - `._(10)^(20)Ne,._(10)^(21 )Ne and _(10)^(22)Ne` the nucleus with the lowest n/p ratio is

Options

A. `._(10)^(22)"Ne"`
B. `._(10)^(21)"Ne"`
C. `._(10)^(20)"Ne"`
D. All of these

Answer

To determine which isotope of Neon has the lowest neutron-to-proton (n/p) ratio among the isotopes \( _{10}^{20}\text{Ne} \), \( _{10}^{21}\text{Ne} \), and \( _{10}^{22}\text{Ne} \), we will follow these steps:

### Step 1: Identify the isotopes and their mass numbers
The isotopes of Neon are:
- \( _{10}^{20}\text{Ne} \) (Mass number = 20)
- \( _{10}^{21}\text{Ne} \) (Mass number = 21)
- \( _{10}^{22}\text{Ne} \) (Mass number = 22)

### Step 2: Determine the number of protons (p) and neutrons (n) for each isotope
The number of protons (p) in each isotope is equal to the atomic number (Z), which is 10 for Neon.

Now, we calculate the number of neutrons (n) using the formula:
\[ n = A - Z \]
where A is the mass number.

1. For \( _{10}^{20}\text{Ne} \):
- Protons (p) = 10
- Neutrons (n) = \( 20 - 10 = 10 \)

2. For \( _{10}^{21}\text{Ne} \):
- Protons (p) = 10
- Neutrons (n) = \( 21 - 10 = 11 \)

3. For \( _{10}^{22}\text{Ne} \):
- Protons (p) = 10
- Neutrons (n) = \( 22 - 10 = 12 \)

### Step 3: Calculate the n/p ratio for each isotope
Now, we calculate the n/p ratio for each isotope:

1. For \( _{10}^{20}\text{Ne} \):
\[ \text{n/p ratio} = \frac{n}{p} = \frac{10}{10} = 1.0 \]

2. For \( _{10}^{21}\text{Ne} \):
\[ \text{n/p ratio} = \frac{n}{p} = \frac{11}{10} = 1.1 \]

3. For \( _{10}^{22}\text{Ne} \):
\[ \text{n/p ratio} = \frac{n}{p} = \frac{12}{10} = 1.2 \]

### Step 4: Compare the n/p ratios
Now we compare the n/p ratios we calculated:
- \( _{10}^{20}\text{Ne} \): n/p = 1.0
- \( _{10}^{21}\text{Ne} \): n/p = 1.1
- \( _{10}^{22}\text{Ne} \): n/p = 1.2

### Conclusion
The isotope with the lowest n/p ratio is \( _{10}^{20}\text{Ne} \).

### Final Answer
The nucleus with the lowest n/p ratio is \( _{10}^{20}\text{Ne} \).

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