Neutron in thermal ewuilibrium with matter at `27^(@)C` can be throught to behave like ideal gas. Assuming them to gave speed of `v_("rns")`, what is therir De broglie wavelength `lambda` (in mm). Fill `((156)/(11)) lambda` in the OMR shee. (Take `m_(n) = 1.69 xx 10^(-27) kg. k = 1.44 xx 10^(-23) J//K, h = 6.60 xx 10^(-34) Jsec`]

Answer

2

Explanation

`v_(max) = sqrt((3kT)/(m)), lambda = h/p rarr lambda = (h)/(m_(n) xx v_(rms)) = (h)/(sqrt(3kTm_(n))) rArr lambda = (6.6 x 10^(-34))/(sqrt(3xx1.44xx10^(-23)xx1.69xx10^(-27)xx300)) = (2.2 xx 10^(-10))/(1.2 xx 1.3)`
`rArr (156)/(11)lambda = (156 xx 2.2 xx 10^(-10))/(11 xx 1.2 xx 1.3) = (220 xx 10^(-10))/(11) = (22)/(11) nm = 2`