Choose the correct statement

Options

A. Ionisation energy of H is equal to `._(1)H^(2)`
B. Ionisation energy of `._(1)H^(1)` is greater than `._(1)H^(2)`
C. Ionisation energy of `._(1)H^(2)` is greater than `._(1)H^(1)`
D. IE of `._(1)H^(1)` may be greater than or less than `._(1)H^(2)`

Answer

To solve the question regarding the ionization energy of hydrogen isotopes, we can follow these steps:

### Step 1: Understand Ionization Energy
Ionization energy is defined as the amount of energy required to remove the outermost electron from an atom. For hydrogen-like atoms, the formula for the energy of an electron in the nth orbit is given by:

\[ E_n = -\frac{13.6 \, Z^2}{n^2} \]

where \(Z\) is the atomic number and \(n\) is the principal quantum number (orbit number).

### Step 2: Identify the Isotopes
In this case, we are comparing two isotopes of hydrogen:
- **Hydrogen-1 (¹H)**, which has an atomic number \(Z = 1\).
- **Deuterium (²H)**, which is also an isotope of hydrogen and has the same atomic number \(Z = 1\).

### Step 3: Calculate Ionization Energy for Each Isotope
Using the formula for ionization energy:

1. For **Hydrogen-1 (¹H)**:
\[ \text{Ionization Energy}_{¹H} = -E_n = \frac{13.6 \, (1^2)}{n^2} = \frac{13.6}{n^2} \]

2. For **Deuterium (²H)**:
\[ \text{Ionization Energy}_{²H} = -E_n = \frac{13.6 \, (1^2)}{n^2} = \frac{13.6}{n^2} \]

### Step 4: Compare the Ionization Energies
From the calculations, we can see that both isotopes have the same formula for ionization energy since they have the same atomic number and the same value of \(n\) for the ground state (which is 1).

Thus, we conclude:
\[ \text{Ionization Energy}_{¹H} = \text{Ionization Energy}_{²H} \]

### Step 5: Choose the Correct Statement
Based on our findings, the correct statement is:
- The ionization energy of hydrogen (¹H) is equal to the ionization energy of deuterium (²H).

### Final Answer
The correct option is:
- **The ionization energy of hydrogen is equal to that of deuterium (¹H = ²H).**

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