Consider the hydrogen atom as described by the bohr model. the nucleus of the hydrogen atom is a single proton. the electron rotates in a circular orbit about this nucleus. in the n = 5, orbit the electron is 1.32 10-9 m from the nucleus and it rotates with an angular speed of 3.30 1014 rad/s. determine the electron's centripetal acceleration in m/s2.

Explanation:

It is given that the atom is hydrogen. And, its electron rotates in n = 5 orbit with angular speed .

Radius of circular path = m

Hence, first calculate the tangential speed as follows.

          Tangential speed = radius × angular speed

                                        =

As formula to calculate time period is as follows.

                  T = sec

Also,     frequency =

So, for n = 5 and z = 1 the value of frequency is as follows.

             frequency =

                                   =  

                                   = Hz

As formula to calculate centripetal acceleration is as follows.

where,           v = linear speed

                      r = radius

                v =

                   =      

                   =            

Hence, the centripetal acceleration will be as follows.

                            =

                            =

Thus, we can conclude that the electron's centripetal acceleration is .

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