12 g of coal contains approximately 6 × 1023 atoms of carbon.
How many atoms would be in 1 kg of carbon?
Show your working.

5*10^25 atoms of carbon

Explanation:

Check from the periodic table:

M(carbon) = 12.01 g/mol

Convert kg into g:

1 kg = 1000 g

Calculate the number of moles of carbon:

n(carbon) = (1000 g) ÷ (12.01 g/mol) = 83.26 mol

Convert moles into number of particles:

#(carbon) = n × NA = 83.26 mol × 6*10^23

= 5*10^25 particles

Note: NA represents the Avogadro's Number, which has the value 6.02*10^23 particles/mol.

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explanation:

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .