Helium atom is two times heavier than hydrogen molecule. At `25^@ C`, the kinetic energy of He atom is

Options

A. Double than hydrogen
B. Same than hydrogen
C. Four times than hydrogen
D. Half than hydrogen

Answer

To find the kinetic energy of a helium atom at 25°C, we can use the formula for the kinetic energy of an ideal gas, which is given by:

\[ KE = \frac{3}{2} nRT \]

Where:
- \( KE \) is the kinetic energy,
- \( n \) is the number of moles,
- \( R \) is the universal gas constant (approximately \( 8.314 \, \text{J/mol·K} \)),
- \( T \) is the temperature in Kelvin.

### Step 1: Convert the temperature from Celsius to Kelvin
To convert the temperature from Celsius to Kelvin, we use the formula:

\[ T(K) = T(°C) + 273.15 \]

Given that \( T = 25°C \):

\[ T = 25 + 273.15 = 298.15 \, K \]

### Step 2: Determine the number of moles of helium
Since we are dealing with a single helium atom, we can consider it as 1 mole of helium atoms for the calculation of kinetic energy.

### Step 3: Substitute the values into the kinetic energy formula
Now we can substitute the values into the kinetic energy formula. Since we are considering 1 mole of helium, \( n = 1 \):

\[ KE = \frac{3}{2} (1) (8.314 \, \text{J/mol·K}) (298.15 \, K) \]

### Step 4: Calculate the kinetic energy
Now we perform the calculation:

\[ KE = \frac{3}{2} \times 8.314 \times 298.15 \]

Calculating this step by step:

1. Calculate \( 8.314 \times 298.15 \):
\[ 8.314 \times 298.15 \approx 2478.75 \, \text{J} \]

2. Now, multiply by \( \frac{3}{2} \):
\[ KE = \frac{3}{2} \times 2478.75 \approx 3718.125 \, \text{J} \]

### Final Answer
Thus, the kinetic energy of a helium atom at 25°C is approximately \( 3718.125 \, \text{J} \).