The bacterial growth follows the rate law, dN/dt = kN where k is a constant and 'N' is the number of bacteria cell at any time. If the population of bacteria (number of cell) is doubled in 5 min find the time in which the population will be eight times of the initial one?

A piece of wood from an archaeological sample has 5.0 counts min^-1 per gram of C-14, while a fresh sample of wood has a count of 15.0 min^-1g^-1. If half-life of C-14 is 5770 yr, the age of the archaeological sample is

• 8,500 yr

• 9,200 yr

• 10,000 yr

• 11,000 yr

403.

Two gases X (molecular weight M_x) and Y (molecular weight M_y; M_Y > M_X) are at the same temperature T in two different containers. Their root mean square velocities are C_X and C_Y respectively. If the average kinetic energies per molecule of two gases X and Y are E_X and E_Y respectively then which of the following realation(s) is (are) true?

• E_X > E_Y

• C_X > C_Y

• E_X = E_Y = (3/2) RT

• E_X = E_Y = (3/2) k_BT

A plot of ln K against 1/T (abscissa) is expected to be a straight line with an intercept on ordinate axis equal to:

• $\frac{∆\mathrm{S}°}{2.303\mathrm{R}}$

• $\frac{∆\mathrm{S}°}{\mathrm{R}}$

• $-\frac{∆\mathrm{S}°}{\mathrm{R}}$

• R x$∆$S^o

If n_t number of radio atoms are present at time t, the following expression will be a constant

• $\frac{{\mathrm{n}}_{\mathrm{t}}}{\mathrm{t}}$

• $\ln \frac{{\mathrm{n}}_{\mathrm{t}}}{\mathrm{t}}$

• $\frac{\mathrm{d}}{\mathrm{dt}}(\ln \mathrm{nt})$

• $\mathrm{t}·{\mathrm{n}}_{\mathrm{t}}$

The following graph shows how t_1/2 (half-life) of a reactant, R changes with the initial reactant concentration a_0. The order of the reaction will be

• 0

• 1

• 2

• 3

The time taken for 10% completion of a first order reaction is 20 min. Then, for 19% completion, the reaction will take

• 40 min

• 60 min

• 30 min

• 50 min

The half-life of a radioactive element is 10 h. How much will be left after 4 h in 1 g atom sample?

• 45.6 x 10²³ atom

• 4.56 x 10²³ atom

• 4.56 x 10²¹ atom

• 4.56 10²⁰ atom

Radioactivity of a sample (Z = 22) decreases 90% after 10 yr. What will be the half-life of the sample? 

• 5 yr

• 2 yr

• 3 yr

• 10 yr

In the reaction 3A → 2B, rate of reaction $+\frac{\mathrm{d}\left(\mathrm{B}\right)}{\mathrm{dt}}$ is equal to

• $-\frac{1}{3}\frac{\mathrm{d}\left[\mathrm{A}\right]}{\mathrm{dt}}$

• $-\frac{2}{3}\frac{\mathrm{d}\left[\mathrm{A}\right]}{\mathrm{dt}}$

• $+\frac{2\mathrm{d}\left[\mathrm{A}\right]}{\mathrm{dt}}$

• $-\frac{3}{2}\frac{\mathrm{d}\left[\mathrm{A}\right]}{\mathrm{dt}}$