Find the de broglie wavelength of an electron in the ground state of the hydrogen atom.

de Broglie wavelength (λ) is given by the equation

λ = h/p

where h=Planck’s constant whose value is 6.62 x 10^(−34) joule-seconds and

p = momentum of the particle(here electron)

In terms of kinetic energy(E) momentum(p) can be written as,

p=(2mE)^1/2

where m=mass of the particle.

Hence λ becomes

1λ = h(2mE)^-1/2

Given here, E = 13.6 eV = 13.6×1.6×10^-19 joule

m(mass of electron)= 9.1×10^-31 kg

Putting these values in equation (1) we get ,

λ =0.332×10^(-9) meter

=3.32×10^(-10) meter

=3.32 Å

We have to remember a point , which is ' the cart or spring rest on a smooth horizontal track ' , i.e., any frictional force doesn't take place.

Explanation:

a) According to the question the cart is pulled to position A and released, i.e., the velocity of the cart at A initially (say time,t=0) is 0 m/s ,then moves toward position E, where it reverses direction and returns again to position A , in the 2nd phase cart moves along A to E , the cart's velocity increase and again goes to zero at point E and again change the direction, hence

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b) Let's , the distance between two consecutive points is x meter and the spring constant is k N.m  

c) ( File has been attached)

d) Movinf Right

e) Moving left