Problem 12 - University Physics with Modern Physics

Question

(a) The recommended daily allowance (RDA) of the trace metal magnesium is 410 mg/day for males. Express this quantity in \(\mu\)g/day. (b) For adults, the RDA of the amino acid lysine is 12 mg per kg of body weight. How many grams per day should a 75-kg adult receive? (c) A typical multivitamin tablet can contain 2.0 mg of vitamin B\(_2\) (riboflavin), and the RDA is 0.0030 g/day. How many such tablets should a person take each day to get the proper amount of this vitamin, if he gets none from other sources? (d) The RDA for the trace element selenium is 0.000070 g/day. Express this dose in mg/day.

Step-by-Step Solution

Answer

(a) 410,000 μg/day; (b) 0.9 g/day; (c) 2 tablets; (d) 0.070 mg/day.

Step 1: Convert mg to μg for magnesium

The first part of the exercise requires converting 410 mg of magnesium to micrograms (μg). Since 1 mg is equal to 1,000 μg, multiply 410 mg by 1,000 to find the equivalent amount in μg: \[ 410 \, \text{mg} \times 1,000 = 410,000 \, \mu\text{g} \] Therefore, 410 mg of magnesium is equal to 410,000 μg.

Step 2: Calculate lysine intake for a 75-kg adult

To find the grams of lysine per day for a 75-kg adult, multiply the RDA of lysine (12 mg per kg) by the person's body weight:\[ 12 \, \text{mg/kg} \times 75 \, \text{kg} = 900 \, \text{mg} \]Convert the total milligrams to grams by dividing by 1,000:\[ \frac{900 \, \text{mg}}{1,000} = 0.9 \, \text{g} \] Thus, a 75-kg adult should receive 0.9 grams of lysine per day.

Step 3: Determine the number of vitamin B₂ tablets to take

To meet the RDA of 0.0030 g of vitamin B₂ per day, convert this to milligrams first (since 1 g = 1,000 mg):\[ 0.0030 \, \text{g} \times 1,000 = 3.0 \, \text{mg} \]Each tablet contains 2.0 mg of vitamin B₂. Therefore, to find the number of tablets needed to meet the 3.0 mg requirement, divide 3.0 mg by 2.0 mg/tablet:\[ \frac{3.0 \, \text{mg}}{2.0 \, \text{mg/tablet}} = 1.5 \]Since the person cannot take half a tablet, they should take 2 tablets per day to ensure they meet the RDA.

Step 4: Convert selenium from grams to mg

Convert the RDA for selenium from grams to milligrams. Given 0.000070 g/day, multiply by 1,000 to convert to mg:\[ 0.000070 \, \text{g/day} \times 1,000 = 0.070 \, \text{mg/day} \] Thus, the RDA for selenium is 0.070 mg per day.

Key Concepts

Unit Conversion

Converting units is a fundamental skill, especially in nutrition where standard measurements may vary. Suppose we need to convert milligrams (mg) to micrograms (μg) or grams (g) to milligrams (mg). Understanding these conversions helps in interpreting the correct nutritional requirements. For example, 1 milligram (mg) equals 1,000 micrograms (μg). Hence, to convert 410 mg of magnesium to μg, simply multiply by 1,000, resulting in 410,000 μg.

Similarly, when converting grams to milligrams, recall that 1 gram equals 1,000 milligrams. If the recommended daily allowance (RDA) for a nutrient is provided in grams, multiplying by 1,000 will convert it into milligrams. Accurate conversions ensure that we maintain the intended dietary intake, considering the vast differences these seemingly small units represent.

Trace Elements

Trace elements are essential minerals required in minute amounts for proper body functioning. They include selenium, magnesium, zinc, and others, each serving vital biological roles.

For instance, magnesium is critical in energy production and bone health. The RDA provides the amount needed to help maintain these bodily functions. In males, the RDA for magnesium is 410 mg/day, which emphasizes its importance despite the relatively small amount.

Selenium is another trace element with an RDA of just 0.000070 g/day. Once converted to more familiar units, such as milligrams, it's equivalent to 0.070 mg/day. Even though needed in tiny quantities, the role of selenium in the immune system and in preventing cellular damage is crucial. Understanding trace elements in nutrition helps in grasping their importance in a balanced diet.

Nutrition Calculation

Calculating nutritional needs based on body weight or daily requirements can seem complex, but breaking down calculations step-by-step simplifies it. For example, knowing the RDA of lysine is 12 mg/kg, you can compute the necessary intake for a person weighing 75 kg by multiplying these values:

• 12 mg multiplied by 75 kg equals 900 mg.
• Convert 900 mg to grams by dividing by 1,000, resulting in 0.9 grams.

This approach allows precise tailoring of nutrient intake to individual weight.

Similarly, when determining how many vitamin tablets are needed to meet the RDA, knowing that a single tablet contains 2.0 mg helps in calculation. With an RDA of 3.0 mg, dividing this by the dosage per tablet (2.0 mg) finds the number of tablets required, which in this case is 1.5 tablets. Since half-tablets aren't practical, rounding up to 2 tablets ensures adequate intake. Learning these calculations ensures appropriate nutritional consumption and avoids under- or overdosing essential nutrients.