a
(a) \({\lambda _{neutron}} \propto \frac{1}{{\sqrt T }}\)

==> \(\frac{{{\lambda _1}}}{{{\lambda _2}}} = \sqrt {\frac{{{T_2}}}{{{T_1}}}} \)

==>\(\frac{\lambda }{{{\lambda _2}}} = \sqrt {\frac{{(273 + 927)}}{{(273 + 27)}}} = \sqrt {\frac{{1200}}{{300}}} = 2\)

==>\({\lambda _2} = \frac{\lambda }{2}.\)