`2,8,20,50,82,` மற்றும் `126` புரோட்டான்கள் அல்லது நியூட்ரான்கள் கொண்ட நியூக்லைடுகள் விதிவிலக்கு என்று கண்டறியப்பட்டுள்ளது...

The numbers 2,8,20,28,50,82,126 are called as

It has been found that nuclides with 2,8,20,50,82, and 126 protons or neutrons are exceptionally stable. These numbers are refferd to as the magic numbers and their existance has led to.

Nuclei with magic no. of proton Z=2,8,20,28,50,52 and magic no. of neutrons N=2,8,20,28,50,82 and 126 are found to be stable. (i) Verify this by calculating the proton separation energy S_(p) for .^(120)Sn (Z=50) and .^(121)Sb =(Z=51) . The proton separation energy for a nuclide is the minimum energy required to separated the least tightly bound proton form a nucleus of that nuclide. It is given by S_(p)=(M_(z-1,N)+M_(H)-M_(Z,N))c^(2) . given .^(119)Sn =118.9058u, .^(120) Sn =119.902199u, .^(121)Sb=120.903824u, .^(1)H=1.0078252u (ii) what does the existence of magic number indicate?

A manufacturer produces three products x,y,z which he sells in two markets ,Annual sales are indicated below: {:("Market",,"products",),(I,"10,000","2,000","18,000"),(II,"6,000","20,000","8,000"):} (A) if unit sale prices of x,y and z are Rs. 2.50, Rs. 1.50 and Rs. 1.00, respectively , find the total revenue algebra . (b) if the unit costs of the above three commodities are Rs. 2.00,Rs. 1.00 and 50 paise respectively, find the gross profit.

If 40@8 = 50, 30@3 = 100 and 10@2 = 50, then find the value of 20@5 = ?

Find the sum of the following A.P.'s : (i) 3,8,13, .... to 20 terms. (ii) 1,4,7,......... to 50 terms. (iii) 8,5,2, .... to 25 terms. (iv) (a+b), (2a+3b), (3b+5b), ........ to n terms.

Study the following information to answer the questions given below it. A number sorting machine, when given an input of numbers, rearranges the numbers in a particular manner step by step indicated below-- till all the numbers are arranged in a particular order. {:("input : 29 2 15 5 20 11 50 105 28 19 30 140"),("Step I : 2 29 15 5 20 11 50 105 28 19 30 140"),("Step II : 2 140 15 5 20 11 50 105 28 19 30 29"),("Step III : 2 140 5 15 20 11 50 105 28 19 30 29"),("Step IV : 2 140 5 105 20 11 50 15 28 19 30 29 "),("Step V : 2 140 5 105 11 20 50 15 28 19 30 29"),("Step VI : 2 140 5 105 11 50 20 15 28 19 30 29"),("Step VII: 2 140 5 105 11 50 15 20 28 19 30 29"),("Step VIII : 2 140 5 11 50 15 30 28 19 20 29"),("Step IX: 2 140 5 105 11 50 15 30 19 28 20 29"),(" Step X: 2 140 5 105 11 50 15 30 19 29 20 28"):} How many steps would be required in getting the final output for the following input ? Input : 10, 4, 1, 9, 8, 12