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Show that ""(92)^(238)U cannot spontaneo...

Show that `""_(92)^(238)U` cannot spontaneosly emit a proton. Given :
`""_(92)^(238)U=238.05079u, ""_(91)^(237)Pa=237.05121u, ""_(1)^(1)H=1.00783u`

Text Solution

Verified by Experts

The possible reaction is :
`""_(92)^(238)U rarr ""_(91)^(237)Pa+""_(1)^(1)H`
If the reaction takes place then Q - value of the reaction is :
Q- value `=[M_(U)-M)(Pa)-M_(H)]xxc^(2)`
`[238.05079-237.05121-1.00783]uxxc^(2)`
`=[-0.00825u]xx931.5(MeV)/(u)=-7.68MeV`
As Q - value is `-ve`, the reaction is endothermic and needs energy to be supplied. So, the reaction cannot take place spontaneously by itself.
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