Cobalt-60 is a radioactive isotope that is commonly used for cancer radiation th

Question

Cobalt-60 is a radioactive isotope that is commonly used for cancer radiation therapy. The cobalt-60 atom decays to the stable nickel-60 atom, releasing a beta particle (electron) and energy in the form of gamma rays:

60Co60Ni++

If you captured the energy from the decay of a 1.19 g pellet of isotopically pure cobalt-60, how long could you run a 80.0 W light bulb?

The relevant masses are as follows:

Gamma rays are massless.

Express your answer to three significant figures and include the appropriate units.

Explanation / Answer

Lets see

The mass of Nickel-60+mass of electron = 59.930788 + 0.000549 = 59.931337 g/mol

Now

Mass lossed when Co-60 converts to Ni-60

59.933819 - (59.930788 + 0.000549) = 0.002482 g = 0.002482 x 10-3 Kg

Now we know that

E =mc2

= 0.002482 x 10-3 Kg x (3 x 108 m/s)2 = 2.2338 x 1011 J

But we have only 1.19 g of Co-60 , then

E = 2.2338 x 1011 J x (1.19/59.933819)

= 4.43526 x 109 J

Now

A Joule is a watt-second , Now we can find how many seconds we can power that 80.0 W light bulb

Then

4.43526 x 109 Watt.second / 80.0 Watt = 5.54 x 107 seconds

1 hour = 3600 seconds

so

5.54 x 107 seconds / 3600 s/Hr = 1.54 x 104 Hrs

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