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Chapter 4: Q57E (page 138)

In the Bohr model of the hydrogen atom, the electron can have only certain velocities. Obtain a formula for the allowed velocities, then obtain a numerical value for the highest speed possible.

Short Answer

Expert verified

The equation for the allowed velocity of the electron is q24蟺蔚0/nand the numeric value of the maximum allowed velocity isrole="math" localid="1659758061348" 2.18脳106m/s.

Step by step solution

01

Bohr Model.

The expression for the velocity for the electron in the Bohr model of hydrogen is given by,

v2=q24蟺蔚0mr1r

The expression for the radius of the hydrogen atom of the Bohr model is given by,

r=(4蟺蔚0)d2n2mq2

02

Use the expression of velocity and radius for calculation.

The expression for the velocity of the electron is evaluated as,

v2=q24蟺蔚0mr1(4蟺蔚0)d2n2)mq2=q24蟺蔚0/n

The velocity of the electron is calculated as,

role="math" localid="1659758442389" v=q24蟺蔚0hn=1.6脳10-9C24蟺8.85脳10-12C2/N.m21.0546脳10-34J.s1=2.18脳106m/s

Therefore, the equation for the allowed velocity of the electron isq24蟺蔚0/nand the numeric value of the maximum allowed velocity is2.18脳106m/s.

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