For a reaction $\frac{1}{2}A\to 2B$, rate of disappearance of 'A' is related to the rate of appearance of 'B' by the expression:

1. $-\frac{d\left[A\right]}{dt}=4\frac{d\left[B\right]}{dt}$

2. $-\frac{d\left[A\right]}{dt}=\frac{1}{2}\frac{d\left[B\right]}{dt}$

3. $-\frac{d\left[A\right]}{dt}=\frac{1}{4}\frac{d\left[B\right]}{dt}$

4. $-\frac{d\left[A\right]}{dt}=\frac{d\left[B\right]}{dt}$

For a first-order reaction $A\to P$, rate constant (k) [dependent on temperature (T)] was found
to follow the equation \(log \ k \ = \ (-2000)\frac{1}{T} \ + \ 6.0\). The pre-exponential factor A and
the activation energy $E_a$, respectively, are:

1. $1.0\times {10}^6$ $s^{-1}$ $and$ $9.2$ $kJ$ $mo{l}^{-1}$

2. $6.0$ $s^{-1}$ $and$ $16.6$ $kJ$ $mo{l}^{-1}$

3. $1.0\times {10}^6$ $s^{-1}$ $and$ $16.6$ $kJ$ $mo{l}^{-1}$

4. $1.0\times {10}^6$ $s^{-1}$ $and$ $38.3$ $kJ$ $mo{l}^{-1}$

Plots showing the variation of the rate constant (K) with temperature (T) are given below. The plot that follows Arrhenius equation is:

1.   

2.  

3.   

4.  

The time for half-life period of a certain reaction A$\to$Products is 1 hour. When the initial concentration of the reactant 'A', is 2.0 mol $L^{-1}$, how much time does it take for its concentration to change from 0.50 to 0.25 mol $L^{-1}$ if it is a zero-order reaction?

1. 1 h

2. 4 h

3. 0.5 h

4. 0.25 h

The radionuclide ${}_{90}{}^{234}Th$ undergoes two successive $\beta$-decays followed by one $\alpha$-decay. the atomic number and the mass number respectively of the resulting radionucleide are:

(1) 92 and 234

(2) 94 and 230

(3) 90 and 230

(4) 92 and 230

A radioactive element has a half-life of 20 minute. How much time should elapse before the element is reduced to 1/8 its original value?

(1) 40 minute

(2) 60 minute

(3) 80 minute

(4) 160 minute

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 $5.8<mspace\; width="1em"></mspace>\mathrm{x}<mspace\; width="1em"></mspace>{10}^{-2}<mspace\; width="1em"></mspace>{\mathrm{s}}^{-1}$. The order of the reaction is : 

1. First order

2. Zero order

3. Second order

4. Third order