An electron is trapped in a one$-$dimensional infinite potential well. For what $($a$)$ higher quantum number and $($b$)$ lower quantum number is the corresponding energy difference equal to $5$ times the energy difference $\backslash ($ E$\_\{65\}\backslash )$ between the levels $\backslash ($ n$\_\{6\}\backslash )$ and $\backslash ($ n$\_\{5\}\backslash )?($c$)$ Can a pair of adjacent levels have an energy difference equal to $\backslash (4$ E$\_\{65\}\backslash )?$

$($a$)$ Number

Units

$($b$)$ Number

Units

$($c$)$