The ratio of mass of an electron to that of the mass of hydrogen atom is

Options

A. `1 : 3871`
B. `1: 1837`
C. `1 : 1296`
D. `1 : 3781`

Answer

To find the ratio of the mass of an electron to the mass of a hydrogen atom, we can follow these steps:

### Step 1: Identify the mass of an electron
The mass of an electron is given as:
\[ m_e = 9.1 \times 10^{-31} \text{ kg} \]

### Step 2: Identify the mass of a hydrogen atom
A hydrogen atom consists of one proton and one electron. However, since the mass of the electron is negligible compared to the mass of the proton, we can approximate the mass of the hydrogen atom as the mass of the proton. The mass of a proton is given as:
\[ m_H \approx 1.67 \times 10^{-27} \text{ kg} \]

### Step 3: Set up the ratio
The ratio of the mass of an electron to the mass of a hydrogen atom can be expressed as:
\[ \text{Ratio} = \frac{m_e}{m_H} \]

### Step 4: Substitute the values
Substituting the values we have:
\[ \text{Ratio} = \frac{9.1 \times 10^{-31}}{1.67 \times 10^{-27}} \]

### Step 5: Perform the calculation
Now, we can perform the calculation:
\[ \text{Ratio} = \frac{9.1}{1.67} \times \frac{10^{-31}}{10^{-27}} \]
\[ = \frac{9.1}{1.67} \times 10^{-4} \]
Calculating the numerical part:
\[ \frac{9.1}{1.67} \approx 5.45 \]
Thus,
\[ \text{Ratio} \approx 5.45 \times 10^{-4} \]

### Step 6: Express the ratio in simplest form
To express this in the form of a ratio:
\[ \text{Ratio} \approx \frac{1}{1837} \]

### Conclusion
Therefore, the ratio of the mass of an electron to that of the mass of a hydrogen atom is:
\[ 1 : 1837 \]