Calculate the root mean square speed of hydrogen molecule at 500 k ( mass of proton=1.67×10^-27 kg and K=1.38×10-23 j/molecule K)

Molecular Theory of Gases Numericals  12 class physics numericals  12 class physics problems

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00:00Numerical number 9 of unit 15 molecular theory of gases is, calculate the root mean square

00:14speed of hydrogen molecule at 500 Kelvin of proton 1.67 into 10 raised power minus 27 kilogram

00:29and Boltzmann constant K is given as 1.38 into 10 raised power minus 23 joule per Kelvin.

00:43So, first of all, we have to find the root mean square speed of hydrogen molecule which is equal to Watt.

01:02Temperature हमें obtained है, that is 500 Kelvin और

01:10proton का जो मास है, वो 1.67 into 10 raised power minus 27 kg अप्तेंड है.

01:20So, mass of hydrogen molecule will be equal to 2 into 1.67 into 10 raised power minus 27 kg.

01:35So, mass of hydrogen molecule will be 3.34 into 10 raised power minus 27 kg.

01:49जब हम 2 को 1.67 के साथ multiply करेंगे, तो हमें answer मिलेगा 3.34.

01:57So, into 10 raised power minus 27 हम same लिखेंगे.

02:02और बोल्स में लिखेंगे लिखेंगे लिखेंगे का वेल्यू हमें उप्तेंड है, यह वेल्यू हमें लिखेंगे.

02:09we have obtained that is 1.38 into 10 raised power minus 23 Joule per Kelvin and this is

02:23also constant. So, for calculation we will use formula root mean square speed is equal

02:37to under root 3 KT upon M. So, by putting the given values 3 into the value of Boltzmann constant

02:53is 1.38 into 10 raised power minus 23 into temperature which is obtained is 500 Kelvin divided by

03:07mass of hydrogen molecule which is 3.34 into 10 raised power minus 27 kg. So, root mean square

03:21speed will be obtained as under root.

03:26जब हम 3 1.38 और 500 को multiply करवाएंगे आपस में तो हमें answer मिलेगा

03:36under root 2,070 into 10 raised power minus 23 divided by 3.34 into 10 raised power minus

03:5227. So, जब हम 2,070 में से 3.34 divided करवाएंगे तो हमें answer मिलेगा

04:02under root 2,070 into 10 raised power minus 23 यहाँ पर 27 minus का है तो उपर जाकर यह पिलस का हो जाएगा. So,

04:29plus 27. So, root mean square speed will be equal to under root 619.76 into 10 raised power minus 23 plus 27. So,

04:51it will be 4. So, under root of 619.76 will be 24.8949 into 10 raised power, the under root

05:09of 10 raised power 4 is 10 raised power 2 meter per second. So, root mean square speed will

05:21be obtained as 10 raised power 2 को हम ऐसे बलिख सकते हैं कि यह value 100 के

05:29equal होता है. So, जब हम 100 इस value के साथ multiply करवाएंगे तो हमें answer मिलेगा

05:362489.49.49 meter per second. So, this is our final answer.