In the ground state of hydrogen atom, its Bohr radius is `5.3xx10^(-11)m`. The atom is excited such that the radius becomes `21.2xx10^(-11)m`. Find the value of principal quantum number and total energy of the atom in excited state.
Text Solution
AI Generated Solution
To solve the problem, we need to find the principal quantum number (n) and the total energy of the hydrogen atom in its excited state based on the given radii.
### Step 1: Understand the relationship between radius and principal quantum number
The radius (R) of the nth orbit in a hydrogen atom is given by the formula:
\[ R_n = n^2 \cdot R_1 \]
where \( R_1 \) is the Bohr radius for the ground state (n=1).
### Step 2: Set up the relationship using the given radii
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