Assume that the de-Broglie wave associated with an electron can form a standing wave between the atoms arranged in a one-dimensional array with nodes at each of the atomic sites. It is found that one such standing wave is formed, if the distance d between the atoms of the array is 2 mathringA. A similar standing wave is again formed, if d is increased to 2.5 mathringA but not for any intermediate value of d. The energy of the electron is

Question

Assume that the de-Broglie wave associated with an electron can form a standing wave between the atoms arranged in a one-dimensional array with nodes at each of the atomic sites. It is found that one such standing wave is formed, if the distance d between the atoms of the array is 2 mathringA. A similar standing wave is again formed, if d is increased to 2.5 mathringA but not for any intermediate value of d. The energy of the electron is (A) 160 eV (B) 150.8 eV (C) 145 eV (D) 100 eV

Tardigrade Admin · Accepted Answer

de-Broglie wavelength is given by λ=(h/p)=(h/√2 K m) Here, K= Kinetic energy of electron ∴ K=(h2/2 m λ2)=((6.63 × 10-34)2/2(9.1 × 10-31)(10-10)2) =2.415 × 10-17 J K=((2.415 × 10-17/1.6 × 10-19))=150.8 eV

$160 e V$

$150.8 e V$

$145 e V$

$100 e V$

160eV

150.8eV

145eV

100eV

de-Broglie wavelength is given by λ=ph​=2Km​h​ Here, K= Kinetic energy of electron ∴K=2mλ2h2​=2(9.1×10−31)(10−10)2(6.63×10−34)2​ =2.415×10−17J K=(1.6×10−192.415×10−17​)=150.8eV

$160 e V$

$150.8 e V$

$145 e V$

$100 e V$