State the conclusions of Rutherford's \( \alpha \)-particle scattering experiment.
Rutherford's model of the atom replaced Thomson's "plum pudding" model by introducing the nucleus.
Rutherford's experiment concluded the existence of a small, dense, and positively charged nucleus at the center of the atom.
Key conclusions from the \( \alpha \)-particle scattering experiment:
1. Most \( \alpha \)-particles passed through the gold foil, indicating atoms are mostly empty space.
2. A few \( \alpha \)-particles were deflected at small angles, suggesting a positively charged region in the atom.
3. Very few were deflected back, confirming that the nucleus is small, massive, and positively charged.
The circuit shown in the figure contains two ideal diodes \( D_1 \) and \( D_2 \). If a cell of emf 3V and negligible internal resistance is connected as shown, then the current through \( 70 \, \Omega \) resistance (in amperes) is:
(b) Order of the differential equation: $ 5x^3 \frac{d^3y}{dx^3} - 3\left(\frac{dy}{dx}\right)^2 + \left(\frac{d^2y}{dx^2}\right)^4 + y = 0 $