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 = \(\) \(0 . 8\) \(mol\) \(L^{- 1} \left(min\right)^{- 1}\)

A radioactive substance has a rate constant of \(4 \, \text{years}^{-1}\). What is its half-life?

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:

What is the ratio of the time required for 99% completion to the time required for
90% completion of a first-order reaction?
1. \(t_{99 \%}=3 t_{90 \%}\)
2. \(t_{99 \%}=2 t_{90 \%}\)
3. \(t_{99 \%}=4 t_{90 \%}\)
4. \(t_{90 \%}=2 t_{99 \%}\)

Find the half-life of a first-order reaction if 30% of the reactant decomposes in 40 min.

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 \(\mathrm{60 s^{- 1}}\). The time required to reduce the initial concentration of the reactant to its 1/16 value is: