In the Bohr model of the hydrogen atom, an electron (mass m = 9.1 x 10^-31 kg) orbits a proton at a distance of 5.3 x 10^-11 m. The proton pulls on the electron with an electric force of 8.2 x 10^-8 N. How many revolutions per second does the electron make?

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Everyone. In this problem, we're asked to imagine an electron with a mass of 9.1 times 10 to the exponent negative 31 kg revolving around the nucleus of a helium atom held in orbit by the electric force between them at a distance of 0.5 times 10 to the exponent negative 10 m. This electron experiences an electric force of 1.84 times 10 to the exponent negative seven newtons. And we're asked to determine the number of revolutions per second that this electron makes around the nucleus. We have four answer choices all in revolutions per second. Option, a 4.48 times 10 to the exponent 19. Option B 5.29 times 10 to the exponent 14. Option C 2.14 times 10 to the exponent 13. And option D 1.01 times 10 to the exponent 16. So what we're given in this problem is some information about an electric force in a distance. OK. What we're interested in is the number of revolutions per second. So let's recall that the force say when we're talking about spinning or orbiting this force, which we'll call fr gonna be an equal to the mass multiplied the centre acceleration ac and so this is a radial force. Now, this gives an acceleration. It's not gonna give us the revolutions per second that we want. But recall that we can write our acceleration in terms of B I have a speed. So we can write that FR is equal to the mass M multiplied by V squared divided by. OK. So we're getting closer, we just need to write V in terms of omega where Omega is our angular speed. That's what we're really interested in. Well, we call that V is equal to R oh my God. OK. So we can write our equation as FR is equal to the mass um multiplied by R Omega square. By now, we have an equation with a force which we're given with the mass, which we're given with this radius or distance bar which we're given and with Omega, which we're trying to find. OK. So we have only one known in this equation we can go ahead and solve. Now, simplifying on the right hand side, we have R squared divided by R. We're gonna end up with FR is equal to the mass and multiplied by the R radius, sorry R multiplied by Omega squared. Again, we're solving for Omega at this angular speed, we can divide by M multiplied by R to get that Omega squared is equal to the force R divided by M multiplied by R and now we can go ahead substitute in our values and we're gonna take the square root as well to isolate for M or sorry for Omega. So what we get is that Omega is equal to the square root of the force. Now, we're told that we have an electric force of 1.84 times 10 to the exponent negative avenue. So that's what we use in the numerator. And this is gonna be divided by the mass which were given as 9.1 times 10 to the exponent negative kg. And also in the denominator, we have the radius R which is that distance, say the distance between the nucleus and or, or a restaurant, I should say, all right, so that we were given a 0.5 times 10 to the exponent negative 10 m. Now we work this all out on our calculator. What we're gonna get is that Omega is equal to approximately 6. times 10 to the exponent 16. You may be looking at this thinking, OK. That's not one of the answer choices. But remember this is in radiance per second, the question was asking us to use revolutions per second. So what we're gonna do is take this value, they are 6.35921 oops types tend to be exponent 16 radiance per second. We're gonna multiply multiplied by one revolution for every two P radiates. OK. One revolution divided by two py radium. When we do that, the unit of radium will divide it. We're gonna be left with the unit of radiant per second, which we can calculate to be about 1.01 21 times 10 to the exponent 16 revolutions per se. So that is the answer we were looking for that is the number of revolutions per second that this electron makes around the nucleus. And if we compare this to our answer choices, rounding to three significant digits, we can see that the correct answer is option D 1.01 times 10 to the exponent 16 revolutions per second. Thanks everyone for watching. I hope this video helped see you in the next one.

In the Bohr model of the hydrogen atom, an electron (mass m = 9.1 x 10^-31 kg) orbits a proton at a distance of 5.3 x 10^-11 m. The proton pulls on the electron with an electric force of 8.2 x 10^-8 N. How many revolutions per second does the electron make?

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Key Concepts

Centripetal Force

Electric Force

Angular Velocity