The half-life of ⁹²U₂₃₈ against \(\alpha\)-decay is 4.5 × 10⁹ year.  The time taken in a year for the decay of the 15/16 part of this isotope will be:

1. $9.0\times {10}^9$

2. $1.8\times {10}^{10}$

3. $4.5\times {10}^9$

4. $2.7\times {10}^{10}$

A radioactive isotope has a half-life of 10 day. If today there are 125 g of it left, what was its original weight 40 day earlier?

(1) 600 g

(2) 1000 g

(3) 1250 g

(4) 2000 g

Two radioisotopes P and Q of atomic weight 10 and 20 respectively are mixed in equal amount by weight. After 20 days, their weight ratio is found to be 1:4. Isotope P has a half-life of 10 day. The half-life of isotope Q is:

(1) zero

(2) 5 day

(3) 20 day

(4) infinite

The rate constant of a reaction is $5.8 \mathrm{x} {10}^{-2} {\mathrm{s}}^{-1}$. The order of the reaction is : 

1. First order

2. Zero order

3. Second order

4. Third order

For a chemical reaction $\mathrm{A}\to$ product, the postulated mechanism of the reaction is as follows.

$\mathrm{A}\underset{{\mathrm{k}}_2}{\overset{{\mathrm{k}}_1}{\rightleftharpoons }}3\mathrm{B}\underset{\mathrm{R}.\mathrm{D}.\mathrm{S}}{\overset{{\mathrm{k}}_3}{\to }}{\mathrm{C}}_{}$
If the rate constants for individual reactions are  k₁, k₂ and k₃, and activation energies are 
\(E_{a_{1}} = 180 \ kJ \ mol^{-1}, \)
\( E_{a_{2}} = 90 \ kJ \ mol^{-1}, \)
\( E_{a_{3}} = 40 \ kJ \ mol^{-1}\)
then overall activation energy for the reaction given above is

1. 70 kJ mol^-1

2. -10 kJ mol^-1

3. 310 kJ mol^-1

4. 130 kJ mol^-1

The activation energy for a simple chemical reaction
A $\to$ B is E_a in the forward direction.
The activation energy for the reverse reaction:

1. Can be less than or greater than E_a

2. Is always double of E_a

3. Is negative of E_a

4. Is always less than E_a

3A $\to$ B + C

It would be a zero order reaction when :

(1) The rate of reaction is proportional to square of concentration of A

(2) The rate of reaction remains same at any concentration of A

(3) The rate remains unchanged at any concentration of B and C

(4) The rate of reaction doubles if concentration of B is increased to double.

If the rate of the reaction is equal to the rate constant, the order of the reaction is : 

(1) 3

(2) 0

(3) 1

(4) 2

The temperature dependence of rate constant (k) of a chemical reaction is written in terms of Arrhenius equation, k = Ae^-Ea/RT . Activation energy E_a of the reaction can be calculated by plotting : 

(1) log vs 1 / log T

(2) k vs T

(3) k vs 1 / log T

(4) log k vs 1 / T

The rate constant (in mol L⁻¹ s⁻¹) for a zero-order reaction with an initial concentration of 0.02 M and a half-life of 100 seconds is:

1. $$\(1.0 \times 10^{-4}\)
2. $\mathrm{}$\(2.0 \times 10^{-4}\)
3. $\mathrm{}$\(2.0 \times 10^{-3}\)
4. $\mathrm{}$\(1.0 \times 10^{-2}\)