A freshly prepared radioactive source of half life 2 hours 30 minutes emits radiation which is 64 times the permissible safe level. The minimum time, after which it would be possible to work safely with source, will be __________hours.

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Answered by

Vishal Baghel | Contributor-Level 10

4 months ago

t_1/2= 2hr 30 min

Radiation intensity a disintegrations / sec (Activity)

As, $A = \frac{A_{0}}{{2^{t}}^{\frac{t}{2}}}$

For safe working, $A = \frac{A_{0}}{64} \Rightarrow \frac{A_{0}}{64} = \frac{A_{0}}{2^{\frac{t}{t_{\frac{1}{2}}}}}$

$\Rightarrow t = 6 t_{\frac{1}{2}} = 6 \times 2.5 h r$

= 15

t1/2 = 2hr 30 minRadiation intensity a disintegrations / sec (Activity)As,  <!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1025" DrawAspect="Content" ObjectID="_1814862236"> </o:OLEObject></xml><! [endif]-> <math> <mrow> <mi>A</mi> <mo>=</mo> <mfrac> <mrow> <msub> <mrow> <mi>A</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> </mrow> <mrow> <msup> <mrow> <msup> <mrow> <mn>2</mn> </mrow> <mrow> <mi>t</mi> </mrow> </msup> </mrow> <mrow> <mfrac bevelled="true"> <mrow> <mi>t</mi> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> </mrow> </msup> </mrow> </mfrac> </mrow> </math> For safe working, <math> <mrow> <mi>A</mi> <mo>=</mo> <mfrac> <mrow> <msub> <mrow> <mi>A</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> </mrow> <mrow> <mn>6</mn> <mn>4</mn> </mrow> </mfrac> <mo>⇒</mo> <mfrac> <mrow> <msub> <mrow> <mi>A</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> </mrow> <mrow> <mn>6</mn> <mn>4</mn> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <msub> <mrow> <mi>A</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> </mrow> <mrow> <msup> <mrow> <mn>2</mn> </mrow> <mrow> <mfrac bevelled="true"> <mrow> <mi>t</mi> </mrow> <mrow> <msub> <mrow> <mi>t</mi> </mrow> <mrow> <mfrac bevelled="true"> <mrow> <mn>1</mn> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> </mrow> </msub> </mrow> </mfrac> </mrow> </msup> </mrow> </mfrac> </mrow> </math> <!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1026" DrawAspect="Content" ObjectID="_1814862237"> </o:OLEObject></xml><! [endif]->  <math> <mrow> <mo>⇒</mo> <mi>t</mi> <mo>=</mo> <mn>6</mn> <msub> <mrow> <mi>t</mi> </mrow> <mrow> <mfrac bevelled="true"> <mrow> <mn>1</mn> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> </mrow> </msub> <mo>=</mo> <mn>6</mn> <mo>×</mo> <mn>2</mn> <mo>.</mo> <mn>5</mn> <mi>h</mi> <mi>r</mi> </mrow> </math>                          <!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1027" DrawAspect="Content" ObjectID="_1814862238"> </o:OLEObject></xml><! [endif]-> = 15

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A freshly prepared radioactive source of half life 2 hours 30 minutes emits radiation which is 64 times the permissible safe level. The minimum time, after which it would be possible to work safely with source, will be __________hours.

1 Answer

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