Which level of the single ionized carbon has the same energy as the ground state energy of hydrogen atom?

Calculate the time interval between 33% decay and 67% decay if half-life of a substance is 20 minutes.

The half-life of Au¹⁹⁸ is 2.7 days. The activity of 1.50 mg of Au¹⁹⁸ if its atomic weight is 198 g mol^$$-$$1 is, (N_a = 6 $$\times$$ 10²³/mol).

A radioactive sample is undergoing $$\alpha$$ decay. At any time t₁, its activity is A and another time t₂, the activity is $${A \over 5}$$. What is the average life time for the sample?