Atoms and Nuclei
- The half-life of a radioactive substance is 30 minutes. The time (in minutes) taken between 40% decay and 85% decay of the same radioactive substance is Answer: 3. 60 Use N=N₀(1/2)^(t/T) and compare the remaining fractions. 40% decayed means 60% remains; 85% decayed means 15% remains. Ratio o... 1
- Given the value of Rydberg constant is 10^7\ m^-1, the wave number of the last line of the Balmer series in hydrogen spectrum will be : Answer: 3. 0.25×10⁷\ m⁻¹ Key idea: barν=R(dfrac12²-dfrac1n²) ; the last Balmer line has n→∞ . barν=R/4=10⁷/4=0.25×10⁷\ m⁻¹ . 1
- When an α-particle of mass 'm' moving with velocity 'v' bombards on a heavy nucleus of charge 'Ze', its distance of closest approach from the nucleus depends on m as : Answer: 1. 1/m Key idea: at the closest approach all kinetic energy becomes electrostatic potential energy. 1/2mv²=k(2e)(Ze)/r₀⇒ r₀=4kZe²/mv... 1