The half-life for radioactive decay of ¹⁴C is 5730 years. A wood sample contains only 80% of the ¹⁴C  .The age of the wood sample would be-

1. 1898 years

2. 1765 years

3. 1931 years

4. 1860 years

For a reaction A → Product, with k = 2.0 × 10^–2 s^–1, if the initial concentration of A is 1.0 mol L^-1, the concentration of A after 100 seconds would be :

The decomposition of sucrose follows the first-order rate law. For this decomposition, t_1/2 is 3.00 hours. The fraction of a sample of sucrose that remains after 8 hours would be:

Given the following observations:

The reaction between A and B is first-order with respect to A and zero-order with respect to B. The values of X and Y are, respectively:

1.  X = 0.2 \(mol\) \(L^{- 1}\); Y = \(\) \(0 . 08\) \(mol\) \(L^{- 1} \left(min\right)^{- 1}\)

2.  X = 0.02 \(mol\) \(L^{- 1}\); Y = \(\) \(0 . 08\) \(mol\) \(L^{- 1} \left(min\right)^{- 1}\)

3.  X = 0.01 \(mol\) \(L^{- 1}\); Y = \(\) \(0 . 8\) \(mol\) \(L^{- 1} \left(min\right)^{- 1}\)

4. X = 0.2 \(mol\) \(L^{- 1}\); Y = \(\) \(0 . 8\) \(mol\) \(L^{- 1} \left(min\right)^{- 1}\)

The rate constant of a radioactive substance is $4$ ${\mathrm{years}}^{-1}$. The value of half-life will be : 

1. 0.05 years

2. 0.17 years

3. 0.26 ${\mathrm{years}}^{-1}$

4. 1.6 years

During a nuclear explosion, one of the products is ⁹⁰Sr with a half-life of 28.1 years. If 1µg of ⁹⁰Sr was absorbed in the bones of a newly born baby instead of calcium, the amount of ⁹⁰Sr that will remain after 10 years in the now grown up child would be -

(Given ,antilog(0.108)=1.28)

1. 0.227 µg 

2. 0.781 µg 

3. 7.81 µg 

4. 2.27 µg 

For the decomposition of azoisopropane to hexane and nitrogen at 543 K, the following data was obtained:

The rate constant of the above reaction would be -

1. 1.21 x 10^-3 s^-1

2. 2.21 x 10^-3 s^-1

3. 3.21 x 10^-3 s^-1

4. 4.21 x 10^-3 s^-1

For a first-order reaction, the relationship between time required for 99% completion to the time required for the completion of 90% of the reaction would be :

$1. {\mathrm{t}}_{99\%} = 3 {\mathrm{t}}_{90\%}$
$2. {\mathrm{t}}_{99\% }= 2 {\mathrm{t}}_{90\%}$
$3. {\mathrm{t}}_{99\% }= 4 {\mathrm{t}}_{90\%}$
$4. {\mathrm{t}}_{90\%} = 2{\mathrm{t}}_{99\%}$

A first-order reaction takes 40 min for 30% decomposition. Half life of the reaction is-

1. 55.9 min

2. 77.9 min

3. 63.9 min

4. 80.9 min

The rate constant for a first-order reaction is $60 {\mathrm{s}}^{-1}$. The time required to reduce the initial concentration of the reactant to its 1/16 value is-

1. $5.64\times {10}^{-2} \mathrm{s}$

2. $6.64\times {10}^{-2} \mathrm{s}$

3. $4.62\times {10}^{-2} \mathrm{s}$

4. $0.14\times {10}^{-2} \mathrm{s}$