Question

1. calculate the frequency (in hz) of a photon with a wavelength of 425nm. a. 7.05 x 10^14 hz b. 3.00 x 10^8 hz c. 7.05 x 10^11 d. 4.25 x 10^7 hz e. 6.67 x 10^-34 hz 6) how many grams of oxygen are in 3.50 moles of h2o? a. 6.02 x 10^23 molecules b. 1.75 x 10^24 molecules c. 3.50 x 10^23 molecules d. 2.11 x 10^24 molecules e. 2.11 x 10^23 molecules 7) a sample of magnesium consists of 79.0% mg - 24, 10.0%. what is the average atomic mass of magnesium? a. 24.3 amu b. 25.0 amu c. 24.0 amu d. 26.0 amu e. 24.79 amu 8) calculate the de broglie wavelength (in meters) of

Explanation:

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Step1: Convert wavelength to SI unit

The speed - of - light formula is $c = \lambda
u$, where $c = 3.00\times10^{8}\ m/s$ (speed of light in vacuum), $\lambda$ is the wavelength, and $
u$ is the frequency. Given $\lambda=425\ nm = 425\times10^{-9}\ m$.

Step2: Solve for frequency

We can re - arrange the formula $c = \lambda
u$ to $
u=\frac{c}{\lambda}$. Substitute $c = 3.00\times10^{8}\ m/s$ and $\lambda = 425\times10^{-9}\ m$ into the formula: $
u=\frac{3.00\times10^{8}}{425\times10^{-9}}\ Hz\approx7.05\times10^{14}\ Hz$.

In one molecule of $H_2O$, there is 1 oxygen atom. In 1 mole of $H_2O$, there is 1 mole of oxygen atoms. Given 3.50 moles of $H_2O$, the number of moles of oxygen atoms is also 3.50 moles. To find the number of oxygen atoms, we use Avogadro's number $N = nN_A$, where $n = 3.50\ mol$ and $N_A=6.02\times10^{23}\ mol^{-1}$. So $N=(3.50\ mol)\times(6.02\times10^{23}\ mol^{-1}) = 2.11\times10^{24}$ oxygen atoms. But the question asks for the mass of oxygen in grams. The molar mass of oxygen is $M = 16.00\ g/mol$. The mass of oxygen $m=nM$, where $n = 3.50\ mol$ and $M = 16.00\ g/mol$, so $m=(3.50\ mol)\times(16.00\ g/mol)=56.0\ g$. However, if we assume the question is asking for the number of oxygen atoms (there is a mis - match in the options as they are all in number of molecules/atoms), the number of oxygen atoms in 3.50 moles of $H_2O$ is $N = nN_A=(3.50\ mol)\times(6.02\times10^{23}\ mol^{-1})=2.11\times10^{24}$ atoms.

The average atomic mass of an element with isotopes is calculated using the formula $\bar{A}=\sum_{i}x_iA_i$, where $x_i$ is the relative abundance of the $i$ - th isotope and $A_i$ is the mass number of the $i$ - th isotope. For magnesium, if $x_1 = 0.79$ (79.0%) with $A_1 = 24$, $x_2=0.10$ (10.0%) with $A_2 = 25$, and assume the third isotope with abundance $x_3=1-(0.79 + 0.10)=0.11$ and mass number $A_3 = 26$. Then $\bar{A}=(0.79\times24)+(0.10\times25)+(0.11\times26)=18.96 + 2.5+2.86=24.32\approx24.3\ amu$.

Answer:

A. $7.05\times 10^{14}\ Hz$

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