1. Ground state energy of hydrogen

   For hydrogen, $E_n = -\frac{13.6}{n^2}\,\text{eV}$

   In the ground state, the electron is at $n=1$ with energy $E_1 = -13.6\,\text{eV}.$

2. Energy supplied to the atom

   The atom is given $10.2\,\text{eV}$.

   The energy needed to excite the electron from $n=1$ to $n=2$ is $\Delta E_{1\to 2} = E_2 - E_1 = \left(-\frac{13.6}{4}\right)-(-13.6)$ $= -3.4 + 13.6 = 10.2\,\text{eV}.$

   So the supplied energy excites the electron exactly from $n=1$ to $n=2$.

3. Possible emission on de-excitation

   Once the electron is in the $n=2$ state, it can return only to $n=1$.

   Thus only one transition is possible: $2 \to 1$

4. Number of spectral lines emitted

   Since there is only one possible downward transition, the number of emitted spectral lines is $1.$

5. Option check

   • A: $3$ ❌
   • B: $6$ ❌
   • C: $10$ ❌
   • D: $1$ ✅

Therefore, the correct answer is D.