Given below are two statements:
Statement I : Rutherford's gold foil experiment cannot explain the line spectrum of hydrogen atom.
Statement II : Bohr's model of hydrogen atom contradicts Heisenberg's uncertainty principle.
In the light of the above statements, choose the most appropriate answer from the options given below:

We begin by recalling what Rutherford’s nuclear model proposed. In this model electrons were pictured as orbiting the tiny, massive nucleus just as planets orbit the Sun. There was no assumption of quantisation of either radius or energy. According to classical electrodynamics, a charged particle moving in a curved path must continuously radiate energy, so an electron in Rutherford’s orbit would lose energy steadily and spiral into the nucleus. The radiation produced during this continuous energy loss would itself be continuous in wavelength. Hydrogen, however, actually shows a set of sharply defined spectral lines, for example the Balmer series. Rutherford’s model therefore fails to account for the line spectrum.

So, for Statement I we observe that Rutherford’s gold-foil experiment - and the atomic model derived from it - indeed cannot explain the observed discrete spectral lines of hydrogen. Hence Statement I is true.

Next, let us recall Bohr’s postulates. Bohr assumed that the electron in a hydrogen atom moves in a circular orbit of fixed radius $$r_n$$ with a definite linear momentum $$p_n = m v_n$$ such that the angular momentum is quantised:

$$m v_n r_n = n \hbar, \qquad n = 1,2,3,\dots$$

Knowing $$r_n$$ and $$v_n$$ simultaneously means we can in principle know the electron’s position and momentum with arbitrary precision. But quantum mechanics sets a fundamental limit given by Heisenberg’s uncertainty principle:

$$\Delta x \,\Delta p \ge \frac{h}{4\pi}.$$

In Bohr’s picture, $$\Delta x \to 0$$ (because the orbit radius is fixed) and $$\Delta p \to 0$$ (because the speed is fixed), making the product $$\Delta x\,\Delta p \to 0$$, which violates the inequality. Therefore the idealised circular-orbit picture of Bohr is incompatible with the uncertainty principle discovered later. Hence Statement II is also true.

Since both statements are correct, the option that asserts the truth of both is selected.

Hence, the correct answer is Option D.