The sample size always depends on the universe of reference and on the resources available to conduct the survey.
Therefore, the sample size does not depend on the type of questionnaire.
This depends (among other things) on the type of statistical analysis or model that you plan to use (e.g., simple correlation analysis versus confirmatory factor analysis) as well as on the expected effect sizes and other data characteristics (e.g., the amount of missing data to be expected). Therefore, it is almost impossible to give a concrete answer without knowing more about your specific data-analytic strategy.
Sample size means precision, and the required precision depends on the use of the questionnaire. If it is some local research tool used in a couple of experiments, precision doesn't matter so much and you can go with a couple of dozens. In the simplest case, validity is just a correlation.
If the context of use influences lives or careers of people, you must be more precise and test validity on item level. That's when you need item-response models or CFA. These models have many parameters and their number determines the theoretical minimum for sample size. That's when a set of ideal data just solves the equation. The practical minimum I would estimate to be around three to ten times higher than that.
The sample size required in a study depends on a couple of things, mostly: the statistical test you intend to use (test of correlation, regressions, factor analysis, etc), the 'power of the test' you intend to apply, and the 'effect size', and the population variance and size. There are formulas that calculate the sample size (n) according to the statistical test used and the factors mentioned. You have to find out the right formula that apply to the statistical test you are using. If you intend to use several statistical tests, you shoud calculate the sample size needed (n) by each test using the right formula, and then choose the larger sampe size calculated. Of course, we are speaking about random sampling; if your sample is not random, then the formulas do not apply, but can be used as a guidence, and you should use a much larger sample than required by the formulas. There are also some rules of thumb that you sould be aware of. Lastly, you should take into account the missing values and the response rate (if you are using a questionnaire).
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