The kinetic and potential energy (in eV) of electron present in third Bohr's orbit of hydrogen atom are respectively :
A
`-1.51,-3.02`
B
`1.51,-3.02`
C
`-3.02,1.51`
D
`1.51,-1.51`
Text Solution
AI Generated Solution
The correct Answer is:
To find the kinetic and potential energy of an electron in the third Bohr orbit of a hydrogen atom, we can follow these steps:
### Step 1: Identify the quantum number
The question specifies that we are dealing with the third Bohr orbit, which means the principal quantum number \( n = 3 \).
### Step 2: Calculate the total energy
The total energy \( E \) of an electron in a hydrogen atom can be calculated using the formula:
\[
E = -\frac{13.6 \, \text{eV} \cdot Z^2}{n^2}
\]
For hydrogen, the atomic number \( Z = 1 \). Therefore, substituting the values:
\[
E = -\frac{13.6 \, \text{eV} \cdot 1^2}{3^2} = -\frac{13.6 \, \text{eV}}{9} = -1.51 \, \text{eV}
\]
### Step 3: Calculate the kinetic energy
The kinetic energy \( K \) of the electron is related to the total energy \( E \) by the equation:
\[
K = -\frac{E}{2}
\]
Since total energy is negative, we take the modulus:
\[
K = -(-1.51 \, \text{eV}) / 2 = 1.51 \, \text{eV}
\]
### Step 4: Calculate the potential energy
The potential energy \( U \) is given by:
\[
U = 2E
\]
Substituting the value of total energy:
\[
U = 2 \times (-1.51 \, \text{eV}) = -3.02 \, \text{eV}
\]
### Final Answer
Thus, the kinetic and potential energy of the electron in the third Bohr orbit of the hydrogen atom are:
- Kinetic Energy \( K = 1.51 \, \text{eV} \)
- Potential Energy \( U = -3.02 \, \text{eV} \)
