Which is the correct expression for half-life

(1) ${\mathrm{t}}_{1/2}=\log 2$                 

(2) ${\mathrm{t}}_{1/2}=\frac{\mathrm{\lambda }}{\log 2}$
(3) ${\mathrm{t}}_{1/2}=\frac{\mathrm{\lambda }}{\log 2}(2.303)$     

(4) ${\mathrm{t}}_{1/2}=\frac{2.303 \log 2}{\mathrm{\lambda }}$

A nucleus ${}_{\mathrm{Z}}{}^{\mathrm{A}}\mathrm{A}$ emits an $\mathrm{\alpha }$-particle. The resultant nucleus emits a ${\mathrm{\beta }}^{+}$ particle. The respective atomic and mass no. of the final nucleus will be 

1. Z – 3, A – 4           

2. Z – 1, A – 4

3. Z – 2, A – 4           

4. Z, A – 2

The activity of a radioactive sample is 1.6 curie and its half-life is 2.5 days. Its activity after 10 days will be

(1) 0.8 curie       

(2) 0.4 curie

(3) 0.1 curie       

(4) 0.16 curie

In a mean life of a radioactive sample 

(1) About 1/3 of substance disintegrates

(2) About 2/3 of the substance disintegrates

(3) About 90% of the substance disintegrates

(4) Almost all the substance disintegrates

Three fourth of the active decays in a radioactive sample in 3/4 sec. The half life of the sample is 
(1) $\frac{1}{2}$ sec           

(2) 1 sec
(3) $\frac{3}{8}$ sec           

(4) $\frac{3}{4}$ sec

During mean life of a radioactive element, the fraction that disintegrates is:

(1) e           

(2)  $\frac{1}{\mathrm{e}}$
(3) $\frac{\mathrm{e}-1}{\mathrm{e}}$     

(4) $\frac{\mathrm{e}}{\mathrm{e}-1}$

1 Curie is equal to 

(1) $3\times {10}^{10}$ disintegrations/sec

(2) $3.7\times {10}^7$ disintegrations/sec

(3) $5\times {10}^7$ disintegrations/sec

(4) $3.7\times {10}^{10}$ disintegrations/sec

The electron emitted in beta radiation originates from

(1) Inner orbits of atoms

(2) Free electrons existing in nuclei

(3) Decay of a neutron in a nucleus

(4) Photon escaping from the nucleus

When a radioactive substance emits an $\mathrm{\alpha }$-particle, its position in the periodic table is lowered by

(1) One place             

(2) Two places

(3) Three places           

(4) Four places

A radioactive nucleus emits a beta particle. The parent and daughter nuclei are 

(1) Isotopes             

(2) Isotones

(3) Isomers               

(4) Isobars