Which of the following species has maximum charge to mass ratio?

Options

A. `D^+`
B. `H^+`
C. `He^+`
D. `He^(2+)`

Answer

To determine which species has the maximum charge to mass ratio (E/m), we will calculate the charge to mass ratio for each given species. The charge to mass ratio is given by the formula:

\[ \frac{E}{m} = \frac{\text{Charge}}{\text{Mass}} \]

Let's analyze each option step by step:

### Step 1: Calculate E/m for Deuterium Ion (D⁺)
- **Charge (E)**: +1 (since it is D⁺)
- **Mass (m)**: 2 (the mass of deuterium is approximately 2 amu)

\[ \frac{E}{m} = \frac{1}{2} = 0.5 \]

### Step 2: Calculate E/m for Hydrogen Ion (H⁺)
- **Charge (E)**: +1 (since it is H⁺)
- **Mass (m)**: 1 (the mass of hydrogen is approximately 1 amu)

\[ \frac{E}{m} = \frac{1}{1} = 1 \]

### Step 3: Calculate E/m for Helium Ion (He⁺)
- **Charge (E)**: +1 (since it is He⁺)
- **Mass (m)**: 4 (the mass of helium is approximately 4 amu)

\[ \frac{E}{m} = \frac{1}{4} = 0.25 \]

### Step 4: Calculate E/m for Helium Ion (He²⁺)
- **Charge (E)**: +2 (since it is He²⁺)
- **Mass (m)**: 4 (the mass remains the same as helium)

\[ \frac{E}{m} = \frac{2}{4} = 0.5 \]

### Step 5: Compare the Charge to Mass Ratios
Now, we will summarize the charge to mass ratios calculated:

- Deuterium Ion (D⁺): 0.5
- Hydrogen Ion (H⁺): 1
- Helium Ion (He⁺): 0.25
- Helium Ion (He²⁺): 0.5

### Conclusion
The species with the maximum charge to mass ratio is the Hydrogen Ion (H⁺) with a ratio of 1.

### Final Answer
**The species with the maximum charge to mass ratio is Hydrogen Ion (H⁺).**

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